Подробное решение
Не могу найти шаги в поиске этой производной.
Но производная
Ответ:
asin(x) /asin(x) log(x) \
x *|------- + -----------|
| x ________|
| / 2 |
\ \/ 1 - x /
$$x^{\operatorname{asin}{\left (x \right )}} \left(\frac{\log{\left (x \right )}}{\sqrt{- x^{2} + 1}} + \frac{1}{x} \operatorname{asin}{\left (x \right )}\right)$$
/ 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 / /
$$x^{\operatorname{asin}{\left (x \right )}} \left(\frac{x \log{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \left(\frac{\log{\left (x \right )}}{\sqrt{- x^{2} + 1}} + \frac{1}{x} \operatorname{asin}{\left (x \right )}\right)^{2} + \frac{2}{x \sqrt{- x^{2} + 1}} - \frac{1}{x^{2}} \operatorname{asin}{\left (x \right )}\right)$$
/ 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 / /
$$x^{\operatorname{asin}{\left (x \right )}} \left(\frac{3 x^{2} \log{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \left(\frac{\log{\left (x \right )}}{\sqrt{- x^{2} + 1}} + \frac{1}{x} \operatorname{asin}{\left (x \right )}\right)^{3} + 3 \left(\frac{\log{\left (x \right )}}{\sqrt{- x^{2} + 1}} + \frac{1}{x} \operatorname{asin}{\left (x \right )}\right) \left(\frac{x \log{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{2}{x \sqrt{- x^{2} + 1}} - \frac{1}{x^{2}} \operatorname{asin}{\left (x \right )}\right) + \frac{\log{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{3}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{3}{x^{2} \sqrt{- x^{2} + 1}} + \frac{2}{x^{3}} \operatorname{asin}{\left (x \right )}\right)$$