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