Подробное решение
-
Не могу найти шаги в поиске этой производной.
Но производная
Ответ:
/ / / ___\\ \
asin(x)/ ___\ |log\atan\\/ x // asin(x) |
atan \\/ x /*|---------------- + ---------------------------|
| ________ ___ / ___\|
| / 2 2*\/ x *(1 + x)*atan\\/ x /|
\ \/ 1 - x /
$$\left(\frac{\log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)}}{\sqrt{- x^{2} + 1}} + \frac{\operatorname{asin}{\left(x \right)}}{2 \sqrt{x} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}\right) \operatorname{atan}^{\operatorname{asin}{\left(x \right)}}{\left(\sqrt{x} \right)}$$
/ 2 \
|/ / / ___\\ \ |
||2*log\atan\\/ x // asin(x) | |
||------------------ + -------------------------| |
|| ________ ___ / ___\| |
|| / 2 \/ x *(1 + x)*atan\\/ x /| / / ___\\ |
asin(x)/ ___\ |\ \/ 1 - x / x*log\atan\\/ x // 1 asin(x) asin(x) asin(x) |
atan \\/ x /*|------------------------------------------------- + ------------------ + ------------------------------------- - ---------------------------- - ------------------------- - --------------------------|
| 4 3/2 ________ ___ 2 / ___\ 2 2/ ___\ 3/2 / ___\|
| / 2\ ___ / 2 / ___\ 2*\/ x *(1 + x) *atan\\/ x / 4*x*(1 + x) *atan \\/ x / 4*x *(1 + x)*atan\\/ x /|
\ \1 - x / \/ x *(1 + x)*\/ 1 - x *atan\\/ x / /
$$\left(\frac{\left(\frac{2 \log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)}}{\sqrt{- x^{2} + 1}} + \frac{\operatorname{asin}{\left(x \right)}}{\sqrt{x} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}\right)^{2}}{4} + \frac{x \log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{\operatorname{asin}{\left(x \right)}}{2 \sqrt{x} \left(x + 1\right)^{2} \operatorname{atan}{\left(\sqrt{x} \right)}} - \frac{\operatorname{asin}{\left(x \right)}}{4 x \left(x + 1\right)^{2} \operatorname{atan}^{2}{\left(\sqrt{x} \right)}} + \frac{1}{\sqrt{x} \sqrt{- x^{2} + 1} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} - \frac{\operatorname{asin}{\left(x \right)}}{4 x^{\frac{3}{2}} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}\right) \operatorname{atan}^{\operatorname{asin}{\left(x \right)}}{\left(\sqrt{x} \right)}$$
/ 3 \
|/ / / ___\\ \ / / / ___\\ \ / / / ___\\ \ |
||2*log\atan\\/ x // asin(x) | |2*log\atan\\/ x // asin(x) | | 4*x*log\atan\\/ x // asin(x) asin(x) 4 2*asin(x) | |
||------------------ + -------------------------| 3*|------------------ + -------------------------|*|- -------------------- + ----------------------- + ------------------------ - ------------------------------------- + --------------------------| |
|| ________ ___ / ___\| | ________ ___ / ___\| | 3/2 2 2/ ___\ 3/2 / ___\ ________ ___ 2 / ___\| |
|| / 2 \/ x *(1 + x)*atan\\/ x /| / / ___\\ | / 2 \/ x *(1 + x)*atan\\/ x /| | / 2\ x*(1 + x) *atan \\/ x / x *(1 + x)*atan\\/ x / ___ / 2 / ___\ \/ x *(1 + x) *atan\\/ x /| 2 / / ___\\ ___ |
asin(x)/ ___\ |\ \/ 1 - x / log\atan\\/ x // \ \/ 1 - x / \ \1 - x / \/ x *(1 + x)*\/ 1 - x *atan\\/ x / / 3*x *log\atan\\/ x // asin(x) asin(x) 3 3 3 asin(x) 3*\/ x 3*asin(x) 3*asin(x) 3*asin(x) |
atan \\/ x /*|------------------------------------------------- + ---------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------- + -------------------------- + --------------------------- - ---------------------------------------- - ------------------------------------- - -------------------------------------- + ---------------------------- + --------------------------------- + ------------------------- + -------------------------- + --------------------------|
| 8 3/2 8 5/2 ___ 3 / ___\ 3/2 2 / ___\ ________ ________ ________ 3/2 3 3/ ___\ 3/2 3 2/ ___\ 2 2 2/ ___\ 5/2 / ___\|
| / 2\ / 2\ \/ x *(1 + x) *atan\\/ x / 2*x *(1 + x) *atan\\/ x / ___ 2 / 2 / ___\ 2 / 2 2/ ___\ 3/2 / 2 / ___\ 4*x *(1 + x) *atan \\/ x / / 2\ / ___\ 4*x*(1 + x) *atan \\/ x / 8*x *(1 + x) *atan \\/ x / 8*x *(1 + x)*atan\\/ x /|
\ \1 - x / \1 - x / 2*\/ x *(1 + x) *\/ 1 - x *atan\\/ x / 4*x*(1 + x) *\/ 1 - x *atan \\/ x / 4*x *(1 + x)*\/ 1 - x *atan\\/ x / 2*(1 + x)*\1 - x / *atan\\/ x / /
$$\left(\frac{\left(\frac{2 \log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)}}{\sqrt{- x^{2} + 1}} + \frac{\operatorname{asin}{\left(x \right)}}{\sqrt{x} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}\right)^{3}}{8} - \frac{3 \cdot \left(\frac{2 \log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)}}{\sqrt{- x^{2} + 1}} + \frac{\operatorname{asin}{\left(x \right)}}{\sqrt{x} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}\right) \left(- \frac{4 x \log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{2 \operatorname{asin}{\left(x \right)}}{\sqrt{x} \left(x + 1\right)^{2} \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{\operatorname{asin}{\left(x \right)}}{x \left(x + 1\right)^{2} \operatorname{atan}^{2}{\left(\sqrt{x} \right)}} - \frac{4}{\sqrt{x} \sqrt{- x^{2} + 1} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{\operatorname{asin}{\left(x \right)}}{x^{\frac{3}{2}} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}\right)}{8} + \frac{3 x^{2} \log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{\log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{3 \sqrt{x}}{2 \left(- x^{2} + 1\right)^{\frac{3}{2}} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{\operatorname{asin}{\left(x \right)}}{\sqrt{x} \left(x + 1\right)^{3} \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{3 \operatorname{asin}{\left(x \right)}}{4 x \left(x + 1\right)^{3} \operatorname{atan}^{2}{\left(\sqrt{x} \right)}} + \frac{3 \operatorname{asin}{\left(x \right)}}{8 x^{2} \left(x + 1\right)^{2} \operatorname{atan}^{2}{\left(\sqrt{x} \right)}} - \frac{3}{2 \sqrt{x} \sqrt{- x^{2} + 1} \left(x + 1\right)^{2} \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{\operatorname{asin}{\left(x \right)}}{2 x^{\frac{3}{2}} \left(x + 1\right)^{2} \operatorname{atan}{\left(\sqrt{x} \right)}} - \frac{3}{4 x \sqrt{- x^{2} + 1} \left(x + 1\right)^{2} \operatorname{atan}^{2}{\left(\sqrt{x} \right)}} - \frac{3}{4 x^{\frac{3}{2}} \sqrt{- x^{2} + 1} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{3 \operatorname{asin}{\left(x \right)}}{8 x^{\frac{5}{2}} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{\operatorname{asin}{\left(x \right)}}{4 x^{\frac{3}{2}} \left(x + 1\right)^{3} \operatorname{atan}^{3}{\left(\sqrt{x} \right)}}\right) \operatorname{atan}^{\operatorname{asin}{\left(x \right)}}{\left(\sqrt{x} \right)}$$