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The derivative of the function/ x^(sin(4x))

Derivative of x^(sin(4x))

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

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The solution

You have entered [src] 
 sin(4*x)
x
$$x^{\sin{\left(4 x \right)}}$$ 
x^sin(4*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] 
 sin(4*x) /sin(4*x)                    \
x        *|-------- + 4*cos(4*x)*log(x)|
          \   x                        /
$$x^{\sin{\left(4 x \right)}} \left(4 \log{\left(x \right)} \cos{\left(4 x \right)} + \frac{\sin{\left(4 x \right)}}{x}\right)$$
Simplify
The second derivative [src] 
          /                              2                                             \
 sin(4*x) |/sin(4*x)                    \    sin(4*x)                        8*cos(4*x)|
x        *||-------- + 4*cos(4*x)*log(x)|  - -------- - 16*log(x)*sin(4*x) + ----------|
          |\   x                        /        2                               x     |
          \                                     x                                      /
$$x^{\sin{\left(4 x \right)}} \left(\left(4 \log{\left(x \right)} \cos{\left(4 x \right)} + \frac{\sin{\left(4 x \right)}}{x}\right)^{2} - 16 \log{\left(x \right)} \sin{\left(4 x \right)} + \frac{8 \cos{\left(4 x \right)}}{x} - \frac{\sin{\left(4 x \right)}}{x^{2}}\right)$$
Simplify
The third derivative [src] 
          /                              3                                                                                                                                              \
 sin(4*x) |/sin(4*x)                    \                         48*sin(4*x)   12*cos(4*x)     /sin(4*x)                    \ /sin(4*x)   8*cos(4*x)                     \   2*sin(4*x)|
x        *||-------- + 4*cos(4*x)*log(x)|  - 64*cos(4*x)*log(x) - ----------- - ----------- - 3*|-------- + 4*cos(4*x)*log(x)|*|-------- - ---------- + 16*log(x)*sin(4*x)| + ----------|
          |\   x                        /                              x              2         \   x                        / |    2          x                          |        3    |
          \                                                                          x                                         \   x                                      /       x     /
$$x^{\sin{\left(4 x \right)}} \left(\left(4 \log{\left(x \right)} \cos{\left(4 x \right)} + \frac{\sin{\left(4 x \right)}}{x}\right)^{3} - 3 \left(4 \log{\left(x \right)} \cos{\left(4 x \right)} + \frac{\sin{\left(4 x \right)}}{x}\right) \left(16 \log{\left(x \right)} \sin{\left(4 x \right)} - \frac{8 \cos{\left(4 x \right)}}{x} + \frac{\sin{\left(4 x \right)}}{x^{2}}\right) - 64 \log{\left(x \right)} \cos{\left(4 x \right)} - \frac{48 \sin{\left(4 x \right)}}{x} - \frac{12 \cos{\left(4 x \right)}}{x^{2}} + \frac{2 \sin{\left(4 x \right)}}{x^{3}}\right)$$
Simplify
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