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(sin(x))^(2*x)
The derivative of the function/ (sin(x))^(2*x)

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

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

The graph:

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The solution

You have entered [src] 
   2*x   
sin   (x)
$$\sin^{2 x}{\left(x \right)}$$ 
sin(x)^(2*x)
Detail solution

  1. Don't know the steps in finding this derivative.

    But the derivative is

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   2*x    /                2*x*cos(x)\
sin   (x)*|2*log(sin(x)) + ----------|
          \                  sin(x)  /
$$\left(\frac{2 x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 \log{\left(\sin{\left(x \right)} \right)}\right) \sin^{2 x}{\left(x \right)}$$
Simplify
The second derivative [src] 
            /                               2                   2   \
     2*x    |       /x*cos(x)              \    2*cos(x)   x*cos (x)|
2*sin   (x)*|-x + 2*|-------- + log(sin(x))|  + -------- - ---------|
            |       \ sin(x)               /     sin(x)        2    |
            \                                               sin (x) /
$$2 \left(- x - \frac{x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + 2 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right)^{2} + \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{2 x}{\left(x \right)}$$
Simplify
The third derivative [src] 
            /                               3                              /                    2   \        2             3                \
     2*x    |       /x*cos(x)              \      /x*cos(x)              \ |    2*cos(x)   x*cos (x)|   3*cos (x)   2*x*cos (x)   2*x*cos(x)|
2*sin   (x)*|-3 + 4*|-------- + log(sin(x))|  - 6*|-------- + log(sin(x))|*|x - -------- + ---------| - --------- + ----------- + ----------|
            |       \ sin(x)               /      \ sin(x)               / |     sin(x)        2    |       2            3          sin(x)  |
            \                                                              \                sin (x) /    sin (x)      sin (x)               /
$$2 \left(\frac{2 x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 x \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} + 4 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right)^{3} - 6 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right) \left(x + \frac{x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) - 3 - \frac{3 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{2 x}{\left(x \right)}$$
Simplify
The graph
Derivative of (sin(x))^(2*x)
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