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Derivative of 1/(sin(2*x)^2)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
    1    
---------
   2     
sin (2*x)
$$\frac{1}{\sin^{2}{\left(2 x \right)}}$$
1/(sin(2*x)^2)
Detail solution
  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. Let .

      2. The derivative of sine is cosine:

      3. Then, apply the chain rule. Multiply by :

        1. The derivative of a constant times a function is the constant times the derivative of the function.

          1. Apply the power rule: goes to

          So, the result is:

        The result of the chain rule is:

      The result of the chain rule is:

    The result of the chain rule is:


The answer is:

The graph
The first derivative [src]
   -4*cos(2*x)    
------------------
            2     
sin(2*x)*sin (2*x)
$$- \frac{4 \cos{\left(2 x \right)}}{\sin{\left(2 x \right)} \sin^{2}{\left(2 x \right)}}$$
The second derivative [src]
  /         2     \
  |    3*cos (2*x)|
8*|1 + -----------|
  |        2      |
  \     sin (2*x) /
-------------------
        2          
     sin (2*x)     
$$\frac{8 \left(1 + \frac{3 \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}}\right)}{\sin^{2}{\left(2 x \right)}}$$
The third derivative [src]
    /         2     \         
    |    3*cos (2*x)|         
-64*|2 + -----------|*cos(2*x)
    |        2      |         
    \     sin (2*x) /         
------------------------------
             3                
          sin (2*x)           
$$- \frac{64 \left(2 + \frac{3 \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}}\right) \cos{\left(2 x \right)}}{\sin^{3}{\left(2 x \right)}}$$