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Derivative of:
Derivative of cos(x)^2
Derivative of sin(x^3)
Derivative of log(x)^2
Derivative of log(x^2)
Identical expressions
(asint)/(cost)^ two
( arc sinus of e of t) divide by ( co sinus of e of t) squared
( arc sinus of e of t) divide by ( co sinus of e of t) to the power of two
(asint)/(cost)2
asint/cost2
(asint)/(cost)²
(asint)/(cost) to the power of 2
asint/cost^2
(asint) divide by (cost)^2

The derivative of the function/ (asint)/(cost)^2

Derivative of (asint)/(cost)^2

The solution

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asin(t)
-------
   2   
cos (t)

\frac{\operatorname{asin}{\left(t \right)}}{\cos^{2}{\left(t \right)}}

asin(t)/cos(t)^2

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

         1            2*asin(t)*sin(t)
------------------- + ----------------
   ________                  3        
  /      2     2          cos (t)     
\/  1 - t  *cos (t)

\frac{2 \sin{\left(t \right)} \operatorname{asin}{\left(t \right)}}{\cos^{3}{\left(t \right)}} + \frac{1}{\sqrt{1 - t^{2}} \cos^{2}{\left(t \right)}}

Simplify

The second derivative [src]

                /         2   \                             
     t          |    3*sin (t)|                4*sin(t)     
----------- + 2*|1 + ---------|*asin(t) + ------------------
        3/2     |        2    |              ________       
/     2\        \     cos (t) /             /      2        
\1 - t /                                  \/  1 - t  *cos(t)
------------------------------------------------------------
                             2                              
                          cos (t)

\frac{\frac{t}{\left(1 - t^{2}\right)^{\frac{3}{2}}} + 2 \left(\frac{3 \sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right) \operatorname{asin}{\left(t \right)} + \frac{4 \sin{\left(t \right)}}{\sqrt{1 - t^{2}} \cos{\left(t \right)}}}{\cos^{2}{\left(t \right)}}

Simplify

The third derivative [src]

            2      /         2   \                          /         2   \               
         3*t       |    3*sin (t)|                          |    3*sin (t)|               
  -1 + -------   6*|1 + ---------|                        8*|2 + ---------|*asin(t)*sin(t)
             2     |        2    |                          |        2    |               
       -1 + t      \     cos (t) /       6*t*sin(t)         \     cos (t) /               
- ------------ + ----------------- + ------------------ + --------------------------------
          3/2          ________              3/2                       cos(t)             
  /     2\            /      2       /     2\                                             
  \1 - t /          \/  1 - t        \1 - t /   *cos(t)                                   
------------------------------------------------------------------------------------------
                                            2                                             
                                         cos (t)

\frac{\frac{6 t \sin{\left(t \right)}}{\left(1 - t^{2}\right)^{\frac{3}{2}} \cos{\left(t \right)}} + \frac{8 \left(\frac{3 \sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 2\right) \sin{\left(t \right)} \operatorname{asin}{\left(t \right)}}{\cos{\left(t \right)}} + \frac{6 \left(\frac{3 \sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right)}{\sqrt{1 - t^{2}}} - \frac{\frac{3 t^{2}}{t^{2} - 1} - 1}{\left(1 - t^{2}\right)^{\frac{3}{2}}}}{\cos^{2}{\left(t \right)}}

Simplify

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Identical expressions

Derivative of (asint)/(cost)^2

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The solution