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y=x^(sinx)
The derivative of the function/ y=x^(sinx)

Derivative of y=x^(sinx)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 sin(x)
x
xsin⁡(x)x^{\sin{\left(x \right)}} 
d / sin(x)\
--\x      /
dx
ddxxsin⁡(x)\frac{d}{d x} x^{\sin{\left(x \right)}}
Transform
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
02468-8-6-4-2-1010-2020
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 sin(x) /sin(x)                \
x      *|------ + cos(x)*log(x)|
        \  x                   /
xsin⁡(x)(log⁡(x)cos⁡(x)+sin⁡(x)x)x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)
Simplify
The second derivative [src] 
        /                        2                                    \
 sin(x) |/sin(x)                \    sin(x)                   2*cos(x)|
x      *||------ + cos(x)*log(x)|  - ------ - log(x)*sin(x) + --------|
        |\  x                   /       2                        x    |
        \                              x                              /
xsin⁡(x)((log⁡(x)cos⁡(x)+sin⁡(x)x)2−log⁡(x)sin⁡(x)+2cos⁡(x)x−sin⁡(x)x2)x^{\sin{\left(x \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} - \log{\left(x \right)} \sin{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x} - \frac{\sin{\left(x \right)}}{x^{2}}\right)
Simplify
The third derivative [src] 
        /                        3                                                                                                                  \
 sin(x) |/sin(x)                \                    3*sin(x)   3*cos(x)     /sin(x)                \ /sin(x)                   2*cos(x)\   2*sin(x)|
x      *||------ + cos(x)*log(x)|  - cos(x)*log(x) - -------- - -------- - 3*|------ + cos(x)*log(x)|*|------ + log(x)*sin(x) - --------| + --------|
        |\  x                   /                       x           2        \  x                   / |   2                        x    |       3   |
        \                                                          x                                  \  x                              /      x    /
xsin⁡(x)((log⁡(x)cos⁡(x)+sin⁡(x)x)3−3(log⁡(x)cos⁡(x)+sin⁡(x)x)(log⁡(x)sin⁡(x)−2cos⁡(x)x+sin⁡(x)x2)−log⁡(x)cos⁡(x)−3sin⁡(x)x−3cos⁡(x)x2+2sin⁡(x)x3)x^{\sin{\left(x \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3} - 3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) - \log{\left(x \right)} \cos{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{x} - \frac{3 \cos{\left(x \right)}}{x^{2}} + \frac{2 \sin{\left(x \right)}}{x^{3}}\right)
Simplify
The graph
Derivative of y=x^(sinx)
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