Подробное решение
-
Не могу найти шаги в поиске этой производной.
Но производная
Ответ:
2 / 3 \
cos (x) |cos (x) |
(sin(x)) *|------- - 2*cos(x)*log(sin(x))*sin(x)|
\ sin(x) /
$$\left(- 2 \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} \cos{\left(x \right)} + \frac{\cos^{3}{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{\cos^{2}{\left(x \right)}}{\left(x \right)}$$
/ 2 \
2 | / 2 \ 4 |
cos (x) | 2 | cos (x) | 2 cos (x) 2 2 |
(sin(x)) *|- 5*cos (x) + |- ------- + 2*log(sin(x))*sin(x)| *cos (x) - ------- - 2*cos (x)*log(sin(x)) + 2*sin (x)*log(sin(x))|
| \ sin(x) / 2 |
\ sin (x) /
$$\left(\left(2 \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} \cos^{2}{\left(x \right)} + 2 \log{\left(\sin{\left(x \right)} \right)} \sin^{2}{\left(x \right)} - 2 \log{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)} - 5 \cos^{2}{\left(x \right)} - \frac{\cos^{4}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{\cos^{2}{\left(x \right)}}{\left(x \right)}$$
/ 3 \
2 | / 2 \ 2 4 / 2 \ / 4 \ |
cos (x) | | cos (x) | 2 2*cos (x) 2*cos (x) | cos (x) | | 2 cos (x) 2 2 | |
(sin(x)) *|12*sin(x) - |- ------- + 2*log(sin(x))*sin(x)| *cos (x) + --------- + --------- + 3*|- ------- + 2*log(sin(x))*sin(x)|*|5*cos (x) + ------- - 2*sin (x)*log(sin(x)) + 2*cos (x)*log(sin(x))| + 8*log(sin(x))*sin(x)|*cos(x)
| \ sin(x) / sin(x) 3 \ sin(x) / | 2 | |
\ sin (x) \ sin (x) / /
$$\left(- \left(2 \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} \cos^{2}{\left(x \right)} + 3 \cdot \left(2 \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(- 2 \log{\left(\sin{\left(x \right)} \right)} \sin^{2}{\left(x \right)} + 2 \log{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)} + 5 \cos^{2}{\left(x \right)} + \frac{\cos^{4}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) + 8 \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} + 12 \sin{\left(x \right)} + \frac{2 \cos^{2}{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \cos^{4}{\left(x \right)}}{\sin^{3}{\left(x \right)}}\right) \sin^{\cos^{2}{\left(x \right)}}{\left(x \right)} \cos{\left(x \right)}$$