Подробное решение
-
Не могу найти шаги в поиске этой производной.
Но производная
Ответ:
atan(x) /log(acos(x)) atan(x) \
acos (x)*|------------ - -------------------|
| 2 ________ |
| 1 + x / 2 |
\ \/ 1 - x *acos(x)/
$$\left(\frac{\log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x^{2} + 1} - \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{- x^{2} + 1} \operatorname{acos}{\left(x \right)}}\right) \operatorname{acos}^{\operatorname{atan}{\left(x \right)}}{\left(x \right)}$$
/ 2 \
atan(x) |/log(acos(x)) atan(x) \ atan(x) 2*x*log(acos(x)) 2 x*atan(x) |
acos (x)*||------------ - -------------------| + ------------------ - ---------------- - ---------------------------- - -------------------|
|| 2 ________ | / 2\ 2 2 ________ 3/2 |
|| 1 + x / 2 | \-1 + x /*acos (x) / 2\ / 2\ / 2 / 2\ |
\\ \/ 1 - x *acos(x)/ \1 + x / \1 + x /*\/ 1 - x *acos(x) \1 - x / *acos(x)/
$$\left(\left(\frac{\log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x^{2} + 1} - \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{- x^{2} + 1} \operatorname{acos}{\left(x \right)}}\right)^{2} - \frac{2 x \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{x \operatorname{atan}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} + \frac{\operatorname{atan}{\left(x \right)}}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} - \frac{2}{\sqrt{- x^{2} + 1} \left(x^{2} + 1\right) \operatorname{acos}{\left(x \right)}}\right) \operatorname{acos}^{\operatorname{atan}{\left(x \right)}}{\left(x \right)}$$
/ 3 2 2 \
atan(x) |/log(acos(x)) atan(x) \ /log(acos(x)) atan(x) \ / atan(x) 2*x*log(acos(x)) 2 x*atan(x) \ 2*log(acos(x)) atan(x) 2*atan(x) 3 8*x *log(acos(x)) 3*x 3*x*atan(x) 3*x *atan(x) 6*x |
acos (x)*||------------ - -------------------| - 3*|------------ - -------------------|*|- ------------------ + ---------------- + ---------------------------- + -------------------| - -------------- - ------------------- - -------------------- + --------------------------- + ----------------- - ---------------------------- - ------------------- - ------------------- + -----------------------------|
|| 2 ________ | | 2 ________ | | / 2\ 2 2 ________ 3/2 | 2 3/2 3/2 / 2\ / 2\ 2 3 3/2 2 5/2 2 ________ |
|| 1 + x / 2 | | 1 + x / 2 | | \-1 + x /*acos (x) / 2\ / 2\ / 2 / 2\ | / 2\ / 2\ / 2\ 3 \1 + x /*\-1 + x /*acos (x) / 2\ / 2\ / 2\ / 2\ 2 / 2\ / 2\ / 2 |
\\ \/ 1 - x *acos(x)/ \ \/ 1 - x *acos(x)/ \ \1 + x / \1 + x /*\/ 1 - x *acos(x) \1 - x / *acos(x)/ \1 + x / \1 - x / *acos(x) \1 - x / *acos (x) \1 + x / \1 + x /*\1 - x / *acos(x) \-1 + x / *acos (x) \1 - x / *acos(x) \1 + x / *\/ 1 - x *acos(x)/
$$\left(\left(\frac{\log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x^{2} + 1} - \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{- x^{2} + 1} \operatorname{acos}{\left(x \right)}}\right)^{3} - 3 \left(\frac{\log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x^{2} + 1} - \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{- x^{2} + 1} \operatorname{acos}{\left(x \right)}}\right) \left(\frac{2 x \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{x \operatorname{atan}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} - \frac{\operatorname{atan}{\left(x \right)}}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} + \frac{2}{\sqrt{- x^{2} + 1} \left(x^{2} + 1\right) \operatorname{acos}{\left(x \right)}}\right) + \frac{8 x^{2} \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{2 \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{3 x \operatorname{atan}{\left(x \right)}}{\left(x^{2} - 1\right)^{2} \operatorname{acos}^{2}{\left(x \right)}} - \frac{3 x^{2} \operatorname{atan}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{5}{2}} \operatorname{acos}{\left(x \right)}} + \frac{6 x}{\sqrt{- x^{2} + 1} \left(x^{2} + 1\right)^{2} \operatorname{acos}{\left(x \right)}} - \frac{\operatorname{atan}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} - \frac{3 x}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \left(x^{2} + 1\right) \operatorname{acos}{\left(x \right)}} + \frac{3}{\left(x^{2} - 1\right) \left(x^{2} + 1\right) \operatorname{acos}^{2}{\left(x \right)}} - \frac{2 \operatorname{atan}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{acos}^{3}{\left(x \right)}}\right) \operatorname{acos}^{\operatorname{atan}{\left(x \right)}}{\left(x \right)}$$