Derivative of sqrt((1-sin(2x))/(1+sin(2x)))

You have entered [src]

    ______________
   / 1 - sin(2*x) 
  /  ------------ 
\/   1 + sin(2*x)

\sqrt{\frac{- \sin{\left(2 x \right)} + 1}{\sin{\left(2 x \right)} + 1}}

  /    ______________\
d |   / 1 - sin(2*x) |
--|  /  ------------ |
dx\\/   1 + sin(2*x) /

\frac{d}{d x} \sqrt{\frac{- \sin{\left(2 x \right)} + 1}{\sin{\left(2 x \right)} + 1}}

Transform

Detail solution

Let $u = \frac{1 - \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \frac{1 - \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}$ :
1. Apply the quotient rule, which is:
  
  $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
  
  $f{\left(x \right)} = 1 - \sin{\left(2 x \right)}$ and $g{\left(x \right)} = \sin{\left(2 x \right)} + 1$ .
  
  To find $\frac{d}{d x} f{\left(x \right)}$ :
  1. Differentiate $1 - \sin{\left(2 x \right)}$ term by term:
    1. The derivative of the constant $1$ is zero.
    2. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Let $u = 2 x$ .
      2. The derivative of sine is cosine:
        
        $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$ :
        
        The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x$ goes to $1$
        
        So, the result is: $2$
        
        The result of the chain rule is:
        
        $2 \cos{\left(2 x \right)}$
      So, the result is: $- 2 \cos{\left(2 x \right)}$
    The result is: $- 2 \cos{\left(2 x \right)}$
  To find $\frac{d}{d x} g{\left(x \right)}$ :
  1. Differentiate $\sin{\left(2 x \right)} + 1$ term by term:
    1. The derivative of the constant $1$ is zero.
    2. Let $u = 2 x$ .
    3. The derivative of sine is cosine:
      
      $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
    4. Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$ :
      1. The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x$ goes to $1$
        
        So, the result is: $2$
      The result of the chain rule is:
      
      $2 \cos{\left(2 x \right)}$
    The result is: $2 \cos{\left(2 x \right)}$
  Now plug in to the quotient rule:
  
  $\frac{- 2 \cdot \left(1 - \sin{\left(2 x \right)}\right) \cos{\left(2 x \right)} - 2 \left(\sin{\left(2 x \right)} + 1\right) \cos{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}}$
The result of the chain rule is:

$\frac{- 2 \cdot \left(1 - \sin{\left(2 x \right)}\right) \cos{\left(2 x \right)} - 2 \left(\sin{\left(2 x \right)} + 1\right) \cos{\left(2 x \right)}}{2 \sqrt{\frac{1 - \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}} \left(\sin{\left(2 x \right)} + 1\right)^{2}}$
Now simplify:

$\left(-1\right) 2 \frac{1}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} \left|{\frac{\cos{\left(2 x \right)}}{\sin{\left(2 x \right)} - 1}}\right| \cos{\left(2 x \right)}$

The answer is:

\left(-1\right) 2 \frac{1}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} \left|{\frac{\cos{\left(2 x \right)}}{\sin{\left(2 x \right)} - 1}}\right| \cos{\left(2 x \right)}

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    ______________                                                          
   / 1 - sin(2*x)                 /    cos(2*x)     (1 - sin(2*x))*cos(2*x)\
  /  ------------ *(1 + sin(2*x))*|- ------------ - -----------------------|
\/   1 + sin(2*x)                 |  1 + sin(2*x)                     2    |
                                  \                     (1 + sin(2*x))     /
----------------------------------------------------------------------------
                                1 - sin(2*x)

\frac{\sqrt{\frac{- \sin{\left(2 x \right)} + 1}{\sin{\left(2 x \right)} + 1}} \left(- \frac{\left(- \sin{\left(2 x \right)} + 1\right) \cos{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{\cos{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \left(\sin{\left(2 x \right)} + 1\right)}{- \sin{\left(2 x \right)} + 1}

Simplify

The second derivative [src]

                        /                                                 2                                                                                                                                           \
                        |                             /     -1 + sin(2*x)\     2             2      /     -1 + sin(2*x)\                                     2      /     -1 + sin(2*x)\                              |
    ___________________ |                   2         |-1 + -------------| *cos (2*x)   2*cos (2*x)*|-1 + -------------|                                2*cos (2*x)*|-1 + -------------|        2                     |
   / -(-1 + sin(2*x))   |              4*cos (2*x)    \      1 + sin(2*x)/                          \      1 + sin(2*x)/   2*(-1 + sin(2*x))*sin(2*x)               \      1 + sin(2*x)/   4*cos (2*x)*(-1 + sin(2*x))|
  /  ----------------- *|-2*sin(2*x) - ------------ + ------------------------------- - -------------------------------- + -------------------------- + -------------------------------- + ---------------------------|
\/      1 + sin(2*x)    |              1 + sin(2*x)            -1 + sin(2*x)                      1 + sin(2*x)                    1 + sin(2*x)                   -1 + sin(2*x)                                 2      |
                        \                                                                                                                                                                        (1 + sin(2*x))       /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                     -1 + sin(2*x)

\frac{\sqrt{- \frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1}} \left(\frac{\left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} - 1} - \frac{2 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} - 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{4 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - 2 \sin{\left(2 x \right)} - \frac{4 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)}{\sin{\left(2 x \right)} - 1}

Simplify

The third derivative [src]

                        /       /                 2                                         2                     \                         /                 2                                         2                     \                                                                                                                                                                                                                                 /                 2                                         2                     \                                                                                                                                           \         
                        |       |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|                         |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|                                                        3                                                                                                                                   2               /     -1 + sin(2*x)\ |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|                                                                                             2                                             |         
                        |     8*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|                       8*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|                                    /     -1 + sin(2*x)\     2                                                                          2      /     -1 + sin(2*x)\     /     -1 + sin(2*x)\     2        6*|-1 + -------------|*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|     /     -1 + sin(2*x)\              /     -1 + sin(2*x)\              /     -1 + sin(2*x)\     2             2      /     -1 + sin(2*x)\|         
    ___________________ |       |            1 + sin(2*x)         1 + sin(2*x)                             2      |                         |            1 + sin(2*x)         1 + sin(2*x)                             2      |                          2         |-1 + -------------| *cos (2*x)         2                                                      8*cos (2*x)*|-1 + -------------|   6*|-1 + -------------| *cos (2*x)     \      1 + sin(2*x)/ |            1 + sin(2*x)         1 + sin(2*x)                             2      |   4*|-1 + -------------|*sin(2*x)   4*|-1 + -------------|*sin(2*x)   6*|-1 + -------------| *cos (2*x)   8*cos (2*x)*|-1 + -------------||         
   / -(-1 + sin(2*x))   |       \                                                            (1 + sin(2*x))       /   4*(-1 + sin(2*x))     \                                                            (1 + sin(2*x))       /   24*sin(2*x)      24*cos (2*x)    \      1 + sin(2*x)/              24*cos (2*x)*(-1 + sin(2*x))   24*(-1 + sin(2*x))*sin(2*x)               \      1 + sin(2*x)/     \      1 + sin(2*x)/                                     \                                                            (1 + sin(2*x))       /     \      1 + sin(2*x)/              \      1 + sin(2*x)/              \      1 + sin(2*x)/                          \      1 + sin(2*x)/|         
  /  ----------------- *|-4 - ------------------------------------------------------------------------------------- + ----------------- + ------------------------------------------------------------------------------------- + ------------ + --------------- - ------------------------------- - ---------------------------- - --------------------------- - -------------------------------- - --------------------------------- - ---------------------------------------------------------------------------------------------------------- - ------------------------------- + ------------------------------- + --------------------------------- + --------------------------------|*cos(2*x)
\/      1 + sin(2*x)    |                                         -1 + sin(2*x)                                          1 + sin(2*x)                                          1 + sin(2*x)                                       1 + sin(2*x)                 2                          2                              3                              2                                2                                   2                                                         -1 + sin(2*x)                                                           -1 + sin(2*x)                      1 + sin(2*x)              (1 + sin(2*x))*(-1 + sin(2*x))     (1 + sin(2*x))*(-1 + sin(2*x)) |         
                        \                                                                                                                                                                                                                        (1 + sin(2*x))            (-1 + sin(2*x))                 (1 + sin(2*x))                 (1 + sin(2*x))                  (-1 + sin(2*x))                     (-1 + sin(2*x))                                                                                                                                                                                                                                                                 /         
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                             -1 + sin(2*x)

\frac{\sqrt{- \frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1}} \left(- \frac{\left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{3} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} + \frac{6 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} - \frac{6 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} + \frac{4 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)}{\sin{\left(2 x \right)} - 1} - \frac{4 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} - 1} + \frac{8 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} - \frac{8 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} + \frac{4 \left(\sin{\left(2 x \right)} - 1\right)}{\sin{\left(2 x \right)} + 1} - \frac{24 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{24 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 4 + \frac{8 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)}{\sin{\left(2 x \right)} + 1} + \frac{24 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{24 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{8 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)}{\sin{\left(2 x \right)} - 1}\right) \cos{\left(2 x \right)}}{\sin{\left(2 x \right)} - 1}

Simplify

5-th derivative [src]

                        /                                                                                                                             2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         \         
                        |                                          /                 2                                         2                     \       /                 2                                         2                     \      /                 2              2                 4                                          4                             2                             2                              2                       2                              \                           /                 2                                         2                     \      /                 2              2                 4                                          4                             2                             2                              2                       2                              \                                                                                                                                                                                                                                    /                 2                                         2                     \       /                 2                                         2                     \                                                     /                                           2               2                                                  \                                                   /                 2                                         2                     \                                                                                                                                                                                                 /                 2              2                 4                                          4                             2                             2                              2                       2                              \      /                 2                                         2                     \ /                                           2               2                                                  \      /                                           2               2                                                  \                                                     /                 2                                         2                     \                  /                                           2               2                                                  \                                                                                                                                                                                                                       /                 2                                         2                     \                                                                          2           /                 2                                         2                     \                            /                 2                                         2                     \                          /                                           2               2                                                  \                                                                                                                                                                                                                             3           /                 2                                         2                     \                                                               2           /                                           2               2                                                  \                                                                                                                /                                           2               2                                                  \       /                 2                                         2                     \                                                               /                 2                                         2                     \                                                                            /                                           2               2                                                  \                                      /                 2                                         2                     \                                                                                                                       2           /                 2                                         2                     \                            /                 2                                         2                     \                                                                                                                                            /                 2                                         2                     \|         
                        |                                          |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|       |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|      |            8*cos (2*x)    6*sin (2*x)      24*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   24*cos (2*x)*(-1 + sin(2*x))   6*sin (2*x)*(-1 + sin(2*x))   8*cos (2*x)*(-1 + sin(2*x))   36*cos (2*x)*sin(2*x)   36*cos (2*x)*(-1 + sin(2*x))*sin(2*x)|                           |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|      |            8*cos (2*x)    6*sin (2*x)      24*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   24*cos (2*x)*(-1 + sin(2*x))   6*sin (2*x)*(-1 + sin(2*x))   8*cos (2*x)*(-1 + sin(2*x))   36*cos (2*x)*sin(2*x)   36*cos (2*x)*(-1 + sin(2*x))*sin(2*x)|                                                           5                                                                                                       2                                                         2      |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|       |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|                                    3                |     -1 + sin(2*x)    6*sin(2*x)      6*cos (2*x)     6*cos (2*x)*(-1 + sin(2*x))   6*(-1 + sin(2*x))*sin(2*x)|                                                   |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|  /     -1 + sin(2*x)\                          4                                                                                                          2                /     -1 + sin(2*x)\ |            8*cos (2*x)    6*sin (2*x)      24*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   24*cos (2*x)*(-1 + sin(2*x))   6*sin (2*x)*(-1 + sin(2*x))   8*cos (2*x)*(-1 + sin(2*x))   36*cos (2*x)*sin(2*x)   36*cos (2*x)*(-1 + sin(2*x))*sin(2*x)|      |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))| |     -1 + sin(2*x)    6*sin(2*x)      6*cos (2*x)     6*cos (2*x)*(-1 + sin(2*x))   6*(-1 + sin(2*x))*sin(2*x)|      |     -1 + sin(2*x)    6*sin(2*x)      6*cos (2*x)     6*cos (2*x)*(-1 + sin(2*x))   6*(-1 + sin(2*x))*sin(2*x)|                                                     |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|           2      |     -1 + sin(2*x)    6*sin(2*x)      6*cos (2*x)     6*cos (2*x)*(-1 + sin(2*x))   6*(-1 + sin(2*x))*sin(2*x)|                                                                                                                                                                                           2      /     -1 + sin(2*x)\ |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|                           2                          /     -1 + sin(2*x)\     2      |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|       /     -1 + sin(2*x)\ |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|                   2      |     -1 + sin(2*x)    6*sin(2*x)      6*cos (2*x)     6*cos (2*x)*(-1 + sin(2*x))   6*(-1 + sin(2*x))*sin(2*x)|                           2                                                                         3                                    2                                    3                         /     -1 + sin(2*x)\     2      |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|                          4                /     -1 + sin(2*x)\     2      |     -1 + sin(2*x)    6*sin(2*x)      6*cos (2*x)     6*cos (2*x)*(-1 + sin(2*x))   6*(-1 + sin(2*x))*sin(2*x)|                                                               3                    2      /     -1 + sin(2*x)\ |     -1 + sin(2*x)    6*sin(2*x)      6*cos (2*x)     6*cos (2*x)*(-1 + sin(2*x))   6*(-1 + sin(2*x))*sin(2*x)|       |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|                                                        2      |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|                           2                    2      /     -1 + sin(2*x)\ |     -1 + sin(2*x)    6*sin(2*x)      6*cos (2*x)     6*cos (2*x)*(-1 + sin(2*x))   6*(-1 + sin(2*x))*sin(2*x)|          2      /     -1 + sin(2*x)\ |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|                          2                                             3                          /     -1 + sin(2*x)\     2      |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|       /     -1 + sin(2*x)\ |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))|                                    2                                                                           2      /     -1 + sin(2*x)\ |            2*cos (2*x)    (-1 + sin(2*x))*sin(2*x)   2*cos (2*x)*(-1 + sin(2*x))||         
                        |                                      160*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|    64*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|   64*|-sin(2*x) - ------------ + ------------ + --------------- + ------------------------ - ---------------------------- - --------------------------- + --------------------------- + --------------------- - -------------------------------------|                        64*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|   64*|-sin(2*x) - ------------ + ------------ + --------------- + ------------------------ - ---------------------------- - --------------------------- + --------------------------- + --------------------- - -------------------------------------|                                       /     -1 + sin(2*x)\     4                                                                              /     -1 + sin(2*x)\     4               4      /     -1 + sin(2*x)\   384*cos (2*x)*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|   384*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|*sin(2*x)       /     -1 + sin(2*x)\     4        96*|-1 + ------------- + ------------ + --------------- - --------------------------- - --------------------------|*sin(2*x)         2      /     -1 + sin(2*x)\   60*|-sin(2*x) - ------------ + ------------------------ + ---------------------------| *|-1 + -------------|      /     -1 + sin(2*x)\     4           /     -1 + sin(2*x)\               /     -1 + sin(2*x)\               /     -1 + sin(2*x)\     2        40*|-1 + -------------|*|-sin(2*x) - ------------ + ------------ + --------------- + ------------------------ - ---------------------------- - --------------------------- + --------------------------- + --------------------- - -------------------------------------|   80*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|*|-1 + ------------- + ------------ + --------------- - --------------------------- - --------------------------|   96*|-1 + ------------- + ------------ + --------------- - --------------------------- - --------------------------|*sin(2*x)          2      /     -1 + sin(2*x)\   160*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|    192*cos (2*x)*|-1 + ------------- + ------------ + --------------- - --------------------------- - --------------------------|                                                                                                                                             2      /     -1 + sin(2*x)\            560*cos (2*x)*|-1 + -------------|*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|       /     -1 + sin(2*x)\     2                 200*|-1 + -------------| *cos (2*x)*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|   200*|-1 + -------------|*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|*sin(2*x)   192*cos (2*x)*|-1 + ------------- + ------------ + --------------- - --------------------------- - --------------------------|       /     -1 + sin(2*x)\     4               2      /     -1 + sin(2*x)\      /     -1 + sin(2*x)\     4           /     -1 + sin(2*x)\     2           /     -1 + sin(2*x)\     2                 20*|-1 + -------------| *cos (2*x)*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|      /     -1 + sin(2*x)\     4        40*|-1 + -------------| *cos (2*x)*|-1 + ------------- + ------------ + --------------- - --------------------------- - --------------------------|         2      /     -1 + sin(2*x)\       /     -1 + sin(2*x)\     4        200*cos (2*x)*|-1 + -------------|*|-1 + ------------- + ------------ + --------------- - --------------------------- - --------------------------|   384*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|*sin(2*x)          4      /     -1 + sin(2*x)\   384*cos (2*x)*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|       /     -1 + sin(2*x)\     4        200*cos (2*x)*|-1 + -------------|*|-1 + ------------- + ------------ + --------------- - --------------------------- - --------------------------|   160*cos (2*x)*|-1 + -------------|*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|      /     -1 + sin(2*x)\     2                    /     -1 + sin(2*x)\     2                 200*|-1 + -------------| *cos (2*x)*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|   200*|-1 + -------------|*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|*sin(2*x)       /     -1 + sin(2*x)\     2                        2      /     -1 + sin(2*x)\            720*cos (2*x)*|-1 + -------------|*|-sin(2*x) - ------------ + ------------------------ + ---------------------------||         
    ___________________ |             2                            |            1 + sin(2*x)         1 + sin(2*x)                             2      |       |            1 + sin(2*x)         1 + sin(2*x)                             2      |      |            1 + sin(2*x)   1 + sin(2*x)                 3         1 + sin(2*x)                             4                              2                             2                          2                               3           |                           |            1 + sin(2*x)         1 + sin(2*x)                             2      |      |            1 + sin(2*x)   1 + sin(2*x)                 3         1 + sin(2*x)                             4                              2                             2                          2                               3           |            2                 4        |-1 + -------------| *cos (2*x)           4                                2                        400*|-1 + -------------| *cos (2*x)   384*cos (2*x)*|-1 + -------------|                 |            1 + sin(2*x)         1 + sin(2*x)                             2      |       |            1 + sin(2*x)         1 + sin(2*x)                             2      |            140*|-1 + -------------| *cos (2*x)      |      1 + sin(2*x)   1 + sin(2*x)                 2                       3                            2      |            96*sin (2*x)*|-1 + -------------|      |            1 + sin(2*x)         1 + sin(2*x)                             2      |  \      1 + sin(2*x)/   20*|-1 + -------------| *cos (2*x)   16*|-1 + -------------|*sin(2*x)   16*|-1 + -------------|*sin(2*x)   40*|-1 + -------------| *cos (2*x)      \      1 + sin(2*x)/ |            1 + sin(2*x)   1 + sin(2*x)                 3         1 + sin(2*x)                             4                              2                             2                          2                               3           |      |            1 + sin(2*x)         1 + sin(2*x)                             2      | |      1 + sin(2*x)   1 + sin(2*x)                 2                       3                            2      |      |      1 + sin(2*x)   1 + sin(2*x)                 2                       3                            2      |            128*cos (2*x)*|-1 + -------------|       |            1 + sin(2*x)         1 + sin(2*x)                             2      |                  |      1 + sin(2*x)   1 + sin(2*x)                 2                       3                            2      |                                         2                                2                         2                                 576*cos (2*x)*|-1 + -------------|*sin(2*x)                 \      1 + sin(2*x)/ |            1 + sin(2*x)         1 + sin(2*x)                             2      |   320*|-1 + -------------| *cos (2*x)*sin(2*x)       \      1 + sin(2*x)/            |            1 + sin(2*x)         1 + sin(2*x)                             2      |       \      1 + sin(2*x)/ |            1 + sin(2*x)         1 + sin(2*x)                             2      |                          |      1 + sin(2*x)   1 + sin(2*x)                 2                       3                            2      |   160*|-1 + -------------| *cos (2*x)   128*cos (2*x)*|-1 + -------------|   60*|-1 + -------------| *cos (2*x)   40*|-1 + -------------| *cos (2*x)   40*|-1 + -------------| *cos (2*x)*sin(2*x)      \      1 + sin(2*x)/            |            1 + sin(2*x)         1 + sin(2*x)                             2      |   20*|-1 + -------------| *cos (2*x)      \      1 + sin(2*x)/            |      1 + sin(2*x)   1 + sin(2*x)                 2                       3                            2      |   96*sin (2*x)*|-1 + -------------|   200*|-1 + -------------| *cos (2*x)                 \      1 + sin(2*x)/ |      1 + sin(2*x)   1 + sin(2*x)                 2                       3                            2      |       |            1 + sin(2*x)         1 + sin(2*x)                             2      |            384*cos (2*x)*|-1 + -------------|                 |            1 + sin(2*x)         1 + sin(2*x)                             2      |   560*|-1 + -------------| *cos (2*x)                 \      1 + sin(2*x)/ |      1 + sin(2*x)   1 + sin(2*x)                 2                       3                            2      |                 \      1 + sin(2*x)/ |            1 + sin(2*x)         1 + sin(2*x)                             2      |   80*|-1 + -------------| *cos (2*x)*sin(2*x)   40*|-1 + -------------| *cos (2*x)*sin(2*x)       \      1 + sin(2*x)/            |            1 + sin(2*x)         1 + sin(2*x)                             2      |       \      1 + sin(2*x)/ |            1 + sin(2*x)         1 + sin(2*x)                             2      |            400*|-1 + -------------| *cos (2*x)*sin(2*x)   576*cos (2*x)*|-1 + -------------|*sin(2*x)                 \      1 + sin(2*x)/ |            1 + sin(2*x)         1 + sin(2*x)                             2      ||         
   / -(-1 + sin(2*x))   |      960*cos (2*x)    480*sin(2*x)       \                                                            (1 + sin(2*x))       /       \                                                            (1 + sin(2*x))       /      \                                          (1 + sin(2*x))                                     (1 + sin(2*x))                 (1 + sin(2*x))                (1 + sin(2*x))             (1 + sin(2*x))                  (1 + sin(2*x))            /   16*(-1 + sin(2*x))      \                                                            (1 + sin(2*x))       /      \                                          (1 + sin(2*x))                                     (1 + sin(2*x))                 (1 + sin(2*x))                (1 + sin(2*x))             (1 + sin(2*x))                  (1 + sin(2*x))            /    1440*sin (2*x)    1920*cos (2*x)   \      1 + sin(2*x)/              1920*cos (2*x)*(-1 + sin(2*x))   1440*sin (2*x)*(-1 + sin(2*x))       \      1 + sin(2*x)/                            \      1 + sin(2*x)/                 \                                                            (1 + sin(2*x))       /       \                                                            (1 + sin(2*x))       /                \      1 + sin(2*x)/                 \                                    (1 + sin(2*x))          (1 + sin(2*x))               (1 + sin(2*x))       /                         \      1 + sin(2*x)/      \                                                            (1 + sin(2*x))       /                            \      1 + sin(2*x)/                 \      1 + sin(2*x)/               \      1 + sin(2*x)/               \      1 + sin(2*x)/                                      \                                          (1 + sin(2*x))                                     (1 + sin(2*x))                 (1 + sin(2*x))                (1 + sin(2*x))             (1 + sin(2*x))                  (1 + sin(2*x))            /      \                                                            (1 + sin(2*x))       / \                                    (1 + sin(2*x))          (1 + sin(2*x))               (1 + sin(2*x))       /      \                                    (1 + sin(2*x))          (1 + sin(2*x))               (1 + sin(2*x))       /                          \      1 + sin(2*x)/       \                                                            (1 + sin(2*x))       /                  \                                    (1 + sin(2*x))          (1 + sin(2*x))               (1 + sin(2*x))       /   480*(-1 + sin(2*x))*sin(2*x)   960*cos (2*x)*(-1 + sin(2*x))   3840*cos (2*x)*sin(2*x)   3840*cos (2*x)*(-1 + sin(2*x))*sin(2*x)                 \      1 + sin(2*x)/                                               \                                                            (1 + sin(2*x))       /       \      1 + sin(2*x)/                                                           \                                                            (1 + sin(2*x))       /                            \                                                            (1 + sin(2*x))       /                          \                                    (1 + sin(2*x))          (1 + sin(2*x))               (1 + sin(2*x))       /       \      1 + sin(2*x)/                            \      1 + sin(2*x)/      \      1 + sin(2*x)/                 \      1 + sin(2*x)/                 \      1 + sin(2*x)/                                                          \                                                            (1 + sin(2*x))       /      \      1 + sin(2*x)/                                                 \                                    (1 + sin(2*x))          (1 + sin(2*x))               (1 + sin(2*x))       /                \      1 + sin(2*x)/       \      1 + sin(2*x)/                                                 \                                    (1 + sin(2*x))          (1 + sin(2*x))               (1 + sin(2*x))       /       \                                                            (1 + sin(2*x))       /                          \      1 + sin(2*x)/                 \                                                            (1 + sin(2*x))       /       \      1 + sin(2*x)/                                                 \                                    (1 + sin(2*x))          (1 + sin(2*x))               (1 + sin(2*x))       /                                      \                                                            (1 + sin(2*x))       /      \      1 + sin(2*x)/                          \      1 + sin(2*x)/                                                           \                                                            (1 + sin(2*x))       /                            \                                                            (1 + sin(2*x))       /                \      1 + sin(2*x)/                                     \      1 + sin(2*x)/                                               \                                                            (1 + sin(2*x))       /|         
  /  ----------------- *|16 - --------------- - ------------ - ---------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------ + -------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------- + --------------- - ------------------------------- - ------------------------------ - ------------------------------ - ----------------------------------- - ---------------------------------- - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------ - ----------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- - --------------------------------- - ------------------------------------------------------------------------------------------------------------ - ---------------------------------- - -------------------------------- + -------------------------------- + ---------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------- + ---------------------------------- + ---------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------ + ---------------------------- + ----------------------------- + ----------------------- - --------------------------------------- - ------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------- - -------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------ - ----------------------------------- - ---------------------------------- - ---------------------------------- - ---------------------------------- - ------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------- + ---------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------- + ----------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------ + ---------------------------------- + ------------------------------------------------------------------------------------------------- + ----------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------- - ------------------------------------------- + ------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------- + -------------------------------------------- + ------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------|*cos(2*x)
\/      1 + sin(2*x)    |                   2   1 + sin(2*x)                                                      2                                                                            1 + sin(2*x)                                                                                                                                                            1 + sin(2*x)                                                                                                                          1 + sin(2*x)                                          -1 + sin(2*x)                                                                                                                                                           -1 + sin(2*x)                                                                                                                                     2                 4                          4                               5                                3                                    4                                    4                                                                    3                                                                                                  2                                                                    4                                                                    1 + sin(2*x)                                                                                   2                                                                        2                                                                         4                      1 + sin(2*x)                      -1 + sin(2*x)                                     2                                                                                                                                          -1 + sin(2*x)                                                                                                                                                                                                                              -1 + sin(2*x)                                                                                                                                                       -1 + sin(2*x)                                                                                   2                                         (1 + sin(2*x))*(-1 + sin(2*x))                                                                                                      2                                                                              2                               3                            3                                 4                                            3                                                                                  3                                                                                   3                                                                                    3                                                                                                                        2                                                                                                     (1 + sin(2*x))*(-1 + sin(2*x))                                                                   2                2      (1 + sin(2*x))*(-1 + sin(2*x))                    2                2      (1 + sin(2*x))*(-1 + sin(2*x))                                  3                                                                                  3                                                                                     3                                                                                      2                                                                      (1 + sin(2*x))*(-1 + sin(2*x))                                    3                                                                                      2                                                                                                     (1 + sin(2*x))*(-1 + sin(2*x))                                                                   3                                                                    2                                                                    3                                                                (1 + sin(2*x))*(-1 + sin(2*x))                                                                                                                      2                                                                                   2                                                             2                                                                                   2                                                                                           (1 + sin(2*x))*(-1 + sin(2*x))                                                                                  2                                              2                                                                                  2                                            |         
                        \     (1 + sin(2*x))                                                       (-1 + sin(2*x))                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             (1 + sin(2*x))    (1 + sin(2*x))            (-1 + sin(2*x))                  (1 + sin(2*x))                   (1 + sin(2*x))                      (-1 + sin(2*x))                      (-1 + sin(2*x))                                                      (-1 + sin(2*x))                                                                                    (-1 + sin(2*x))                                                      (-1 + sin(2*x))                                                                                                                                                     (-1 + sin(2*x))                                                          (-1 + sin(2*x))                                                           (-1 + sin(2*x))                                                                                            (-1 + sin(2*x))                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           (-1 + sin(2*x))                                                                                                                                                               (-1 + sin(2*x))                                                                 (1 + sin(2*x))                  (1 + sin(2*x))               (1 + sin(2*x))                    (1 + sin(2*x))                              (-1 + sin(2*x))                                                                    (-1 + sin(2*x))                                                                     (-1 + sin(2*x))                                                                      (-1 + sin(2*x))                                                                                                          (-1 + sin(2*x))                                                                                                                                                                                         (1 + sin(2*x)) *(-1 + sin(2*x))                                           (1 + sin(2*x)) *(-1 + sin(2*x))                                                        (-1 + sin(2*x))                                                                    (-1 + sin(2*x))                                                        (1 + sin(2*x))*(-1 + sin(2*x))                                                                        (-1 + sin(2*x))                                                                                                           (1 + sin(2*x))*(-1 + sin(2*x))                                                                        (-1 + sin(2*x))                                                                                                                                                                         (1 + sin(2*x))*(-1 + sin(2*x))                                       (1 + sin(2*x))*(-1 + sin(2*x))                                       (1 + sin(2*x))*(-1 + sin(2*x))                                                                                                                                                                                                       (1 + sin(2*x)) *(-1 + sin(2*x))                                                     (1 + sin(2*x)) *(-1 + sin(2*x))               (1 + sin(2*x))*(-1 + sin(2*x))                                                      (1 + sin(2*x))*(-1 + sin(2*x))                                                                                                                                                                              (1 + sin(2*x))*(-1 + sin(2*x))                 (1 + sin(2*x))*(-1 + sin(2*x))                                                     (1 + sin(2*x))*(-1 + sin(2*x))                                             /         
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    -1 + sin(2*x)

\frac{\sqrt{- \frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1}} \left(- \frac{\left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{5} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{4}} + \frac{20 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{4} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3} \left(\sin{\left(2 x \right)} + 1\right)} - \frac{20 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{4} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{4}} + \frac{40 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{3} \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2} \left(\sin{\left(2 x \right)} + 1\right)} - \frac{60 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{3} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2} \left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{20 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{3} \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3}} - \frac{40 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{3} \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3}} + \frac{200 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{3} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3} \left(\sin{\left(2 x \right)} + 1\right)} - \frac{140 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{3} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{4}} + \frac{40 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 1 + \frac{6 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{6 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} - \frac{40 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} - \frac{80 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)^{2}} + \frac{40 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} + \frac{200 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2} \left(\sin{\left(2 x \right)} + 1\right)} + \frac{400 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2} \left(\sin{\left(2 x \right)} + 1\right)} - \frac{160 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2} \left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{200 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3}} - \frac{320 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3}} + \frac{560 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3} \left(\sin{\left(2 x \right)} + 1\right)} - \frac{400 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{4}} - \frac{200 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 1 + \frac{6 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{6 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} + \frac{200 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 1 + \frac{6 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{6 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} - \frac{16 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{40 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} + \frac{8 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{36 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - \frac{24 \left(\sin{\left(2 x \right)} - 1\right) \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{4}} - \sin{\left(2 x \right)} + \frac{6 \sin^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} - \frac{8 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{36 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} + \frac{24 \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}}\right)}{\sin{\left(2 x \right)} - 1} + \frac{16 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} - 1} + \frac{200 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} + \frac{96 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \sin^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} - \frac{128 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} - \frac{160 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{60 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)^{2}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} - \frac{200 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} - \frac{96 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \sin^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} + \frac{128 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} + \frac{720 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2} \left(\sin{\left(2 x \right)} + 1\right)} + \frac{576 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2} \left(\sin{\left(2 x \right)} + 1\right)} - \frac{560 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3}} - \frac{576 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3}} + \frac{384 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3} \left(\sin{\left(2 x \right)} + 1\right)} - \frac{384 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{4}} - \frac{96 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 1 + \frac{6 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{6 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}}\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{80 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 1 + \frac{6 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{6 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}}\right)}{\sin{\left(2 x \right)} - 1} + \frac{96 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 1 + \frac{6 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{6 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}}\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} - 1} - \frac{192 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 1 + \frac{6 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{6 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} + \frac{192 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 1 + \frac{6 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{6 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} - \frac{16 \left(\sin{\left(2 x \right)} - 1\right)}{\sin{\left(2 x \right)} + 1} + \frac{480 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{1440 \left(\sin{\left(2 x \right)} - 1\right) \sin^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} + \frac{960 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - \frac{3840 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{4}} - \frac{1920 \left(\sin{\left(2 x \right)} - 1\right) \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{5}} + 16 - \frac{64 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)}{\sin{\left(2 x \right)} + 1} - \frac{64 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} + \frac{8 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{36 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - \frac{24 \left(\sin{\left(2 x \right)} - 1\right) \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{4}} - \sin{\left(2 x \right)} + \frac{6 \sin^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} - \frac{8 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{36 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} + \frac{24 \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}}\right)}{\sin{\left(2 x \right)} + 1} - \frac{480 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{1440 \sin^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{960 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} + \frac{3840 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} + \frac{1920 \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{4}} + \frac{64 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)}{\sin{\left(2 x \right)} - 1} + \frac{64 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} + \frac{8 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{36 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - \frac{24 \left(\sin{\left(2 x \right)} - 1\right) \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{4}} - \sin{\left(2 x \right)} + \frac{6 \sin^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} - \frac{8 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{36 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} + \frac{24 \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}}\right)}{\sin{\left(2 x \right)} - 1} + \frac{160 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)^{2}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} + \frac{384 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} - \frac{160 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)^{2}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} - \frac{384 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} + \frac{384 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2} \left(\sin{\left(2 x \right)} + 1\right)} - \frac{384 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3}}\right) \cos{\left(2 x \right)}}{\sin{\left(2 x \right)} - 1}

Simplify

The graph

Derivative of sqrt((1-sin(2x))/(1+sin(2x)))

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of sqrt((1-sin(2x))/(1+sin(2x)))

The graph:

Piecewise:

The solution