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

Derivative of 2*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)
2*x
2xsin⁡(x)2 x^{\sin{\left(x \right)}} 
d /   sin(x)\
--\2*x      /
dx
ddx2xsin⁡(x)\frac{d}{d x} 2 x^{\sin{\left(x \right)}}
Transform
Detail solution

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

    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)}

    So, the result is: 2(log⁡(sin⁡(x))+1)sin⁡sin⁡(x)(x)2 \left(\log{\left(\sin{\left(x \right)} \right)} + 1\right) \sin^{\sin{\left(x \right)}}{\left(x \right)}

The answer is:

2(log⁡(sin⁡(x))+1)sin⁡sin⁡(x)(x)2 \left(\log{\left(\sin{\left(x \right)} \right)} + 1\right) \sin^{\sin{\left(x \right)}}{\left(x \right)}

The graph
02468-8-6-4-2-1010-5050
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   sin(x) /sin(x)                \
2*x      *|------ + cos(x)*log(x)|
          \  x                   /
2xsin⁡(x)(log⁡(x)cos⁡(x)+sin⁡(x)x)2 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)|
2*x      *||------ + cos(x)*log(x)|  - ------ - log(x)*sin(x) + --------|
          |\  x                   /       2                        x    |
          \                              x                              /
2xsin⁡(x)((log⁡(x)cos⁡(x)+sin⁡(x)x)2−log⁡(x)sin⁡(x)+2cos⁡(x)x−sin⁡(x)x2)2 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)                \                    2*sin(x)   3*sin(x)   3*cos(x)     /sin(x)                \ /sin(x)                   2*cos(x)\|
-2*x      *|- |------ + cos(x)*log(x)|  + cos(x)*log(x) - -------- + -------- + -------- + 3*|------ + cos(x)*log(x)|*|------ + log(x)*sin(x) - --------||
           |  \  x                   /                        3         x           2        \  x                   / |   2                        x    ||
           \                                                 x                     x                                  \  x                              //
−2xsin⁡(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)- 2 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 2*x^sin(x)
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