Производная x^(asin(x))^3

Вы ввели

     3   
 asin (x)
x        

$$x^{\operatorname{asin}^{3}{\left (x \right )}}$$

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

   $\left(\log{\left (\operatorname{asin}^{3}{\left (x \right )} \right )} + 1\right) \left(\operatorname{asin}^{3}{\left (x \right )}\right)^{\operatorname{asin}^{3}{\left (x \right )}}$

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Ответ:

$\left(\log{\left (\operatorname{asin}^{3}{\left (x \right )} \right )} + 1\right) \left(\operatorname{asin}^{3}{\left (x \right )}\right)^{\operatorname{asin}^{3}{\left (x \right )}}$

Первая производная

     3    /    3            2          \
 asin (x) |asin (x)   3*asin (x)*log(x)|
x        *|-------- + -----------------|
          |   x             ________   |
          |                /      2    |
          \              \/  1 - x     /

$$x^{\operatorname{asin}^{3}{\left (x \right )}} \left(\frac{3 \operatorname{asin}^{2}{\left (x \right )}}{\sqrt{- x^{2} + 1}} \log{\left (x \right )} + \frac{1}{x} \operatorname{asin}^{3}{\left (x \right )}\right)$$

Вторая производная

     3    /                       2                2                                                   \        
 asin (x) |/asin(x)     3*log(x) \      3      asin (x)   6*log(x)     6*asin(x)     3*x*asin(x)*log(x)|        
x        *||------- + -----------| *asin (x) - -------- - -------- + ------------- + ------------------|*asin(x)
          ||   x         ________|                 2            2         ________              3/2    |        
          ||            /      2 |                x       -1 + x         /      2       /     2\       |        
          \\          \/  1 - x  /                                   x*\/  1 - x        \1 - x /       /        

$$x^{\operatorname{asin}^{3}{\left (x \right )}} \left(\frac{3 x \operatorname{asin}{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} \log{\left (x \right )} + \left(\frac{3 \log{\left (x \right )}}{\sqrt{- x^{2} + 1}} + \frac{1}{x} \operatorname{asin}{\left (x \right )}\right)^{2} \operatorname{asin}^{3}{\left (x \right )} - \frac{6 \log{\left (x \right )}}{x^{2} - 1} + \frac{6 \operatorname{asin}{\left (x \right )}}{x \sqrt{- x^{2} + 1}} - \frac{1}{x^{2}} \operatorname{asin}^{2}{\left (x \right )}\right) \operatorname{asin}{\left (x \right )}$$

Третья производная

     3    /                       3                  3                           2                            2              2                                                /      2                                                   \      2     2                                \
 asin (x) |/asin(x)     3*log(x) \      6      2*asin (x)     6*log(x)     9*asin (x)    18*asin(x)     9*asin (x)     3*asin (x)*log(x)         3    /asin(x)     3*log(x) \ |  asin (x)   6*log(x)     6*asin(x)     3*x*asin(x)*log(x)|   9*x *asin (x)*log(x)   18*x*asin(x)*log(x)|
x        *||------- + -----------| *asin (x) + ---------- + ----------- + ----------- - ----------- - -------------- + ----------------- + 3*asin (x)*|------- + -----------|*|- -------- - -------- + ------------- + ------------------| + -------------------- + -------------------|
          ||   x         ________|                  3               3/2           3/2     /      2\         ________              3/2                 |   x         ________| |      2            2         ________              3/2    |               5/2                      2    |
          ||            /      2 |                 x        /     2\      /     2\      x*\-1 + x /    2   /      2       /     2\                    |            /      2 | |     x       -1 + x         /      2       /     2\       |       /     2\                /      2\     |
          \\          \/  1 - x  /                          \1 - x /      \1 - x /                    x *\/  1 - x        \1 - x /                    \          \/  1 - x  / \                        x*\/  1 - x        \1 - x /       /       \1 - x /                \-1 + x /     /

$$x^{\operatorname{asin}^{3}{\left (x \right )}} \left(\frac{9 x^{2} \operatorname{asin}^{2}{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} \log{\left (x \right )} + \frac{18 x \operatorname{asin}{\left (x \right )}}{\left(x^{2} - 1\right)^{2}} \log{\left (x \right )} + \left(\frac{3 \log{\left (x \right )}}{\sqrt{- x^{2} + 1}} + \frac{1}{x} \operatorname{asin}{\left (x \right )}\right)^{3} \operatorname{asin}^{6}{\left (x \right )} + 3 \left(\frac{3 \log{\left (x \right )}}{\sqrt{- x^{2} + 1}} + \frac{1}{x} \operatorname{asin}{\left (x \right )}\right) \left(\frac{3 x \operatorname{asin}{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} \log{\left (x \right )} - \frac{6 \log{\left (x \right )}}{x^{2} - 1} + \frac{6 \operatorname{asin}{\left (x \right )}}{x \sqrt{- x^{2} + 1}} - \frac{1}{x^{2}} \operatorname{asin}^{2}{\left (x \right )}\right) \operatorname{asin}^{3}{\left (x \right )} + \frac{3 \operatorname{asin}^{2}{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} \log{\left (x \right )} + \frac{6 \log{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{9 \operatorname{asin}^{2}{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{18 \operatorname{asin}{\left (x \right )}}{x \left(x^{2} - 1\right)} - \frac{9 \operatorname{asin}^{2}{\left (x \right )}}{x^{2} \sqrt{- x^{2} + 1}} + \frac{2}{x^{3}} \operatorname{asin}^{3}{\left (x \right )}\right)$$