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

Derivative of x^asin(x)

Function f() - derivative -N order at the point
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The graph:

from to

Piecewise:

The solution

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

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

    But the derivative is

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

The answer is:

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

The graph
02468-8-6-4-2-10102-2
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 asin(x) /asin(x)      log(x)  \
x       *|------- + -----------|
         |   x         ________|
         |            /      2 |
         \          \/  1 - x  /
xasin⁡(x)(log⁡(x)1−x2+asin⁡(x)x)x^{\operatorname{asin}{\left(x \right)}} \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{x}\right)
Simplify
The second derivative [src] 
         /                       2                                        \
 asin(x) |/asin(x)      log(x)  \    asin(x)         2           x*log(x) |
x       *||------- + -----------|  - ------- + ------------- + -----------|
         ||   x         ________|        2          ________           3/2|
         ||            /      2 |       x          /      2    /     2\   |
         \\          \/  1 - x  /              x*\/  1 - x     \1 - x /   /
xasin⁡(x)(xlog⁡(x)(1−x2)32+(log⁡(x)1−x2+asin⁡(x)x)2+2x1−x2−asin⁡(x)x2)x^{\operatorname{asin}{\left(x \right)}} \left(\frac{x \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{x}\right)^{2} + \frac{2}{x \sqrt{1 - x^{2}}} - \frac{\operatorname{asin}{\left(x \right)}}{x^{2}}\right)
Simplify
The third derivative [src] 
         /                       3                                                                                                                                     2       \
 asin(x) |/asin(x)      log(x)  \         3           log(x)           3          2*asin(x)     /asin(x)      log(x)  \ /  asin(x)         2           x*log(x) \   3*x *log(x)|
x       *||------- + -----------|  + ----------- + ----------- - -------------- + --------- + 3*|------- + -----------|*|- ------- + ------------- + -----------| + -----------|
         ||   x         ________|            3/2           3/2         ________        3        |   x         ________| |      2          ________           3/2|           5/2|
         ||            /      2 |    /     2\      /     2\       2   /      2        x         |            /      2 | |     x          /      2    /     2\   |   /     2\   |
         \\          \/  1 - x  /    \1 - x /      \1 - x /      x *\/  1 - x                   \          \/  1 - x  / \            x*\/  1 - x     \1 - x /   /   \1 - x /   /
xasin⁡(x)(3x2log⁡(x)(1−x2)52+(log⁡(x)1−x2+asin⁡(x)x)3+3(log⁡(x)1−x2+asin⁡(x)x)(xlog⁡(x)(1−x2)32+2x1−x2−asin⁡(x)x2)+log⁡(x)(1−x2)32+3(1−x2)32−3x21−x2+2asin⁡(x)x3)x^{\operatorname{asin}{\left(x \right)}} \left(\frac{3 x^{2} \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{x}\right)^{3} + 3 \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{x}\right) \left(\frac{x \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{x \sqrt{1 - x^{2}}} - \frac{\operatorname{asin}{\left(x \right)}}{x^{2}}\right) + \frac{\log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{x^{2} \sqrt{1 - x^{2}}} + \frac{2 \operatorname{asin}{\left(x \right)}}{x^{3}}\right)
Simplify
The graph
Derivative of x^asin(x)
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