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x^(sin(x^3))
The derivative of the function/ x^(sin(x^3))

Derivative of x^(sin(x^3))

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
    / 3\
 sin\x /
x
xsin⁡(x3)x^{\sin{\left(x^{3} \right)}} 
  /    / 3\\
d | sin\x /|
--\x       /
dx
ddxxsin⁡(x3)\frac{d}{d x} x^{\sin{\left(x^{3} \right)}}
Transform
Detail solution

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

    But the derivative is

    (log⁡(sin⁡(x3))+1)sin⁡sin⁡(x3)(x3)\left(\log{\left(\sin{\left(x^{3} \right)} \right)} + 1\right) \sin^{\sin{\left(x^{3} \right)}}{\left(x^{3} \right)}

The answer is:

(log⁡(sin⁡(x3))+1)sin⁡sin⁡(x3)(x3)\left(\log{\left(\sin{\left(x^{3} \right)} \right)} + 1\right) \sin^{\sin{\left(x^{3} \right)}}{\left(x^{3} \right)}

The graph
02468-8-6-4-2-1010-50005000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    / 3\ /   / 3\                      \
 sin\x / |sin\x /      2    / 3\       |
x       *|------- + 3*x *cos\x /*log(x)|
         \   x                         /
xsin⁡(x3)(3x2log⁡(x)cos⁡(x3)+sin⁡(x3)x)x^{\sin{\left(x^{3} \right)}} \left(3 x^{2} \log{\left(x \right)} \cos{\left(x^{3} \right)} + \frac{\sin{\left(x^{3} \right)}}{x}\right)
Simplify
The second derivative [src] 
         /                               2                                                                   \
    / 3\ |/   / 3\                      \       / 3\                                                         |
 sin\x / ||sin\x /      2    / 3\       |    sin\x /          / 3\      4           / 3\          / 3\       |
x       *||------- + 3*x *cos\x /*log(x)|  - ------- + 6*x*cos\x / - 9*x *log(x)*sin\x / + 6*x*cos\x /*log(x)|
         |\   x                         /        2                                                           |
         \                                      x                                                            /
xsin⁡(x3)(−9x4log⁡(x)sin⁡(x3)+6xlog⁡(x)cos⁡(x3)+6xcos⁡(x3)+(3x2log⁡(x)cos⁡(x3)+sin⁡(x3)x)2−sin⁡(x3)x2)x^{\sin{\left(x^{3} \right)}} \left(- 9 x^{4} \log{\left(x \right)} \sin{\left(x^{3} \right)} + 6 x \log{\left(x \right)} \cos{\left(x^{3} \right)} + 6 x \cos{\left(x^{3} \right)} + \left(3 x^{2} \log{\left(x \right)} \cos{\left(x^{3} \right)} + \frac{\sin{\left(x^{3} \right)}}{x}\right)^{2} - \frac{\sin{\left(x^{3} \right)}}{x^{2}}\right)
Simplify
The third derivative [src] 
         /                               3                                                                                                                                                                                                                \
    / 3\ |/   / 3\                      \                                  /   / 3\                      \ /   / 3\                                                         \        / 3\                                                                 |
 sin\x / ||sin\x /      2    / 3\       |         / 3\       3    / 3\     |sin\x /      2    / 3\       | |sin\x /          / 3\          / 3\             4           / 3\|   2*sin\x /        / 3\              3           / 3\       6    / 3\       |
x       *||------- + 3*x *cos\x /*log(x)|  + 9*cos\x / - 27*x *sin\x / - 3*|------- + 3*x *cos\x /*log(x)|*|------- - 6*x*cos\x / - 6*x*cos\x /*log(x) + 9*x *log(x)*sin\x /| + --------- + 6*cos\x /*log(x) - 54*x *log(x)*sin\x / - 27*x *cos\x /*log(x)|
         |\   x                         /                                  \   x                         / |    2                                                           |        3                                                                    |
         \                                                                                                 \   x                                                            /       x                                                                     /
xsin⁡(x3)(−27x6log⁡(x)cos⁡(x3)−54x3log⁡(x)sin⁡(x3)−27x3sin⁡(x3)+(3x2log⁡(x)cos⁡(x3)+sin⁡(x3)x)3−3⋅(3x2log⁡(x)cos⁡(x3)+sin⁡(x3)x)(9x4log⁡(x)sin⁡(x3)−6xlog⁡(x)cos⁡(x3)−6xcos⁡(x3)+sin⁡(x3)x2)+6log⁡(x)cos⁡(x3)+9cos⁡(x3)+2sin⁡(x3)x3)x^{\sin{\left(x^{3} \right)}} \left(- 27 x^{6} \log{\left(x \right)} \cos{\left(x^{3} \right)} - 54 x^{3} \log{\left(x \right)} \sin{\left(x^{3} \right)} - 27 x^{3} \sin{\left(x^{3} \right)} + \left(3 x^{2} \log{\left(x \right)} \cos{\left(x^{3} \right)} + \frac{\sin{\left(x^{3} \right)}}{x}\right)^{3} - 3 \cdot \left(3 x^{2} \log{\left(x \right)} \cos{\left(x^{3} \right)} + \frac{\sin{\left(x^{3} \right)}}{x}\right) \left(9 x^{4} \log{\left(x \right)} \sin{\left(x^{3} \right)} - 6 x \log{\left(x \right)} \cos{\left(x^{3} \right)} - 6 x \cos{\left(x^{3} \right)} + \frac{\sin{\left(x^{3} \right)}}{x^{2}}\right) + 6 \log{\left(x \right)} \cos{\left(x^{3} \right)} + 9 \cos{\left(x^{3} \right)} + \frac{2 \sin{\left(x^{3} \right)}}{x^{3}}\right)
Simplify
The graph
Derivative of x^(sin(x^3))
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