Подробное решение
-
Не могу найти шаги в поиске этой производной.
Но производная
Ответ:
/ / 3*x + 2 \ \
(3*x + 2)*acos(x) | log\log (5)/ -2 - 3*x 3*x + 2 |
log (5)*|- ------------------ + 3*log (5)*log (5)*acos(x)*log(log(5))|
| ________ |
| / 2 |
\ \/ 1 - x /
$$\left(3 \log{\left(5 \right)}^{- 3 x - 2} \log{\left(5 \right)}^{3 x + 2} \log{\left(\log{\left(5 \right)} \right)} \operatorname{acos}{\left(x \right)} - \frac{\log{\left(\log{\left(5 \right)}^{3 x + 2} \right)}}{\sqrt{- x^{2} + 1}}\right) \log{\left(5 \right)}^{\left(3 x + 2\right) \operatorname{acos}{\left(x \right)}}$$
/ / 2 + 3*x \ \
| x*log\log (5)/ |
| 6*log(log(5)) + -------------------- |
| 2 / / 2 + 3*x \ \ |
(2 + 3*x)*acos(x) | 1 - x / 2 + 3*x \ | log\log (5)/ | |
log (5)*|- ------------------------------------ + |3*acos(x) - -----------|*|- ------------------ + 3*acos(x)*log(log(5))|*log(log(5))|
| ________ | ________| | ________ | |
| / 2 | / 2 | | / 2 | |
\ \/ 1 - x \ \/ 1 - x / \ \/ 1 - x / /
$$\left(\left(3 \log{\left(\log{\left(5 \right)} \right)} \operatorname{acos}{\left(x \right)} - \frac{\log{\left(\log{\left(5 \right)}^{3 x + 2} \right)}}{\sqrt{- x^{2} + 1}}\right) \left(3 \operatorname{acos}{\left(x \right)} - \frac{3 x + 2}{\sqrt{- x^{2} + 1}}\right) \log{\left(\log{\left(5 \right)} \right)} - \frac{\frac{x \log{\left(\log{\left(5 \right)}^{3 x + 2} \right)}}{- x^{2} + 1} + 6 \log{\left(\log{\left(5 \right)} \right)}}{\sqrt{- x^{2} + 1}}\right) \log{\left(5 \right)}^{\left(3 x + 2\right) \operatorname{acos}{\left(x \right)}}$$
/ / / 2 + 3*x \ \ / / 2 + 3*x \\ \
| 2 / 2 + 3*x \ / x*(2 + 3*x)\ | log\log (5)/ | / 2 + 3*x \ | x*log\log (5)/| |
| 3*x *log\log (5)/ / 2 + 3*x \ |6 + -----------|*|- ------------------ + 3*acos(x)*log(log(5))|*log(log(5)) 2*|3*acos(x) - -----------|*|6*log(log(5)) + --------------------|*log(log(5))|
| 9*x*log(log(5)) + ----------------------- + log\log (5)/ | 2 | | ________ | | ________| | 2 | |
| 2 2 / / 2 + 3*x \ \ \ 1 - x / | / 2 | | / 2 | \ 1 - x / |
(2 + 3*x)*acos(x) | 1 - x / 2 + 3*x \ 2 | log\log (5)/ | \ \/ 1 - x / \ \/ 1 - x / |
log (5)*|- -------------------------------------------------------------- + |3*acos(x) - -----------| *log (log(5))*|- ------------------ + 3*acos(x)*log(log(5))| - ---------------------------------------------------------------------------- - ------------------------------------------------------------------------------|
| 3/2 | ________| | ________ | ________ ________ |
| / 2\ | / 2 | | / 2 | / 2 / 2 |
\ \1 - x / \ \/ 1 - x / \ \/ 1 - x / \/ 1 - x \/ 1 - x /
$$\left(\left(3 \log{\left(\log{\left(5 \right)} \right)} \operatorname{acos}{\left(x \right)} - \frac{\log{\left(\log{\left(5 \right)}^{3 x + 2} \right)}}{\sqrt{- x^{2} + 1}}\right) \left(3 \operatorname{acos}{\left(x \right)} - \frac{3 x + 2}{\sqrt{- x^{2} + 1}}\right)^{2} \log{\left(\log{\left(5 \right)} \right)}^{2} - \frac{\left(3 \log{\left(\log{\left(5 \right)} \right)} \operatorname{acos}{\left(x \right)} - \frac{\log{\left(\log{\left(5 \right)}^{3 x + 2} \right)}}{\sqrt{- x^{2} + 1}}\right) \left(\frac{x \left(3 x + 2\right)}{- x^{2} + 1} + 6\right) \log{\left(\log{\left(5 \right)} \right)}}{\sqrt{- x^{2} + 1}} - \frac{2 \left(\frac{x \log{\left(\log{\left(5 \right)}^{3 x + 2} \right)}}{- x^{2} + 1} + 6 \log{\left(\log{\left(5 \right)} \right)}\right) \left(3 \operatorname{acos}{\left(x \right)} - \frac{3 x + 2}{\sqrt{- x^{2} + 1}}\right) \log{\left(\log{\left(5 \right)} \right)}}{\sqrt{- x^{2} + 1}} - \frac{\frac{3 x^{2} \log{\left(\log{\left(5 \right)}^{3 x + 2} \right)}}{- x^{2} + 1} + 9 x \log{\left(\log{\left(5 \right)} \right)} + \log{\left(\log{\left(5 \right)}^{3 x + 2} \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}}\right) \log{\left(5 \right)}^{\left(3 x + 2\right) \operatorname{acos}{\left(x \right)}}$$