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

Derivative of (sin(x))^sin(x)

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

The graph:

from to

Piecewise:

The solution

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

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

    But the derivative is

    (log⁡(sin⁡(x))+1)sin⁡sin⁡(x)(x)\left(\log{\left(\sin{\left(x \right)} \right)} + 1\right) \sin^{\sin{\left(x \right)}}{\left(x \right)}

The answer is:

(log⁡(sin⁡(x))+1)sin⁡sin⁡(x)(x)\left(\log{\left(\sin{\left(x \right)} \right)} + 1\right) \sin^{\sin{\left(x \right)}}{\left(x \right)}

The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   sin(x)                                 
sin      (x)*(cos(x)*log(sin(x)) + cos(x))
(log⁡(sin⁡(x))cos⁡(x)+cos⁡(x))sin⁡sin⁡(x)(x)\left(\log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)} + \cos{\left(x \right)}\right) \sin^{\sin{\left(x \right)}}{\left(x \right)}
Simplify
The second derivative [src] 
             /                                          2                        \
   sin(x)    |                           2    2      cos (x)                     |
sin      (x)*|-sin(x) + (1 + log(sin(x))) *cos (x) + ------- - log(sin(x))*sin(x)|
             \                                        sin(x)                     /
((log⁡(sin⁡(x))+1)2cos⁡2(x)−log⁡(sin⁡(x))sin⁡(x)−sin⁡(x)+cos⁡2(x)sin⁡(x))sin⁡sin⁡(x)(x)\left(\left(\log{\left(\sin{\left(x \right)} \right)} + 1\right)^{2} \cos^{2}{\left(x \right)} - \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \sin{\left(x \right)} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{\sin{\left(x \right)}}{\left(x \right)}
Simplify
The third derivative [src] 
             /                                                   2                          /                        2            \\       
   sin(x)    |                                    3    2      cos (x)                       |                     cos (x)         ||       
sin      (x)*|-4 - log(sin(x)) + (1 + log(sin(x))) *cos (x) - ------- - 3*(1 + log(sin(x)))*|log(sin(x))*sin(x) - ------- + sin(x)||*cos(x)
             |                                                   2                          \                      sin(x)         /|       
             \                                                sin (x)                                                              /
((log⁡(sin⁡(x))+1)3cos⁡2(x)−3(log⁡(sin⁡(x))+1)(log⁡(sin⁡(x))sin⁡(x)+sin⁡(x)−cos⁡2(x)sin⁡(x))−log⁡(sin⁡(x))−4−cos⁡2(x)sin⁡2(x))sin⁡sin⁡(x)(x)cos⁡(x)\left(\left(\log{\left(\sin{\left(x \right)} \right)} + 1\right)^{3} \cos^{2}{\left(x \right)} - 3 \left(\log{\left(\sin{\left(x \right)} \right)} + 1\right) \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} + \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) - \log{\left(\sin{\left(x \right)} \right)} - 4 - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{\sin{\left(x \right)}}{\left(x \right)} \cos{\left(x \right)}
Simplify
The graph
Derivative of (sin(x))^sin(x)
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