Подробное решение
-
Не могу найти шаги в поиске этой производной.
Но производная
Ответ:
cos(x) / 2 \
/ 3 \ | / 3 \ 3*x *cos(x)|
\x + 1/ *|- log\x + 1/*sin(x) + -----------|
| 3 |
\ x + 1 /
$$\left(x^{3} + 1\right)^{\cos{\left(x \right)}} \left(\frac{3 x^{2} \cos{\left(x \right)}}{x^{3} + 1} - \log{\left(x^{3} + 1 \right)} \sin{\left(x \right)}\right)$$
/ 2 \
cos(x) |/ 2 \ 4 2 |
/ 3\ || / 3\ 3*x *cos(x)| / 3\ 9*x *cos(x) 6*x *sin(x) 6*x*cos(x)|
\1 + x / *||- log\1 + x /*sin(x) + -----------| - cos(x)*log\1 + x / - ----------- - ----------- + ----------|
|| 3 | 2 3 3 |
|\ 1 + x / / 3\ 1 + x 1 + x |
\ \1 + x / /
$$\left(x^{3} + 1\right)^{\cos{\left(x \right)}} \left(- \frac{9 x^{4} \cos{\left(x \right)}}{\left(x^{3} + 1\right)^{2}} - \frac{6 x^{2} \sin{\left(x \right)}}{x^{3} + 1} + \left(\frac{3 x^{2} \cos{\left(x \right)}}{x^{3} + 1} - \log{\left(x^{3} + 1 \right)} \sin{\left(x \right)}\right)^{2} - \log{\left(x^{3} + 1 \right)} \cos{\left(x \right)} + \frac{6 x \cos{\left(x \right)}}{x^{3} + 1}\right)$$
/ 3 \
cos(x) |/ 2 \ / 2 \ / 2 4 \ 3 2 4 6 |
/ 3\ || / 3\ 3*x *cos(x)| / 3\ | / 3\ 3*x *cos(x)| | / 3\ 6*x*cos(x) 6*x *sin(x) 9*x *cos(x)| 6*cos(x) 54*x *cos(x) 18*x*sin(x) 9*x *cos(x) 27*x *sin(x) 54*x *cos(x)|
\1 + x / *||- log\1 + x /*sin(x) + -----------| + log\1 + x /*sin(x) - 3*|- log\1 + x /*sin(x) + -----------|*|cos(x)*log\1 + x / - ---------- + ----------- + -----------| + -------- - ------------ - ----------- - ----------- + ------------ + ------------|
|| 3 | | 3 | | 3 3 2 | 3 2 3 3 2 3 |
|\ 1 + x / \ 1 + x / | 1 + x 1 + x / 3\ | 1 + x / 3\ 1 + x 1 + x / 3\ / 3\ |
\ \ \1 + x / / \1 + x / \1 + x / \1 + x / /
$$\left(x^{3} + 1\right)^{\cos{\left(x \right)}} \left(\frac{54 x^{6} \cos{\left(x \right)}}{\left(x^{3} + 1\right)^{3}} + \frac{27 x^{4} \sin{\left(x \right)}}{\left(x^{3} + 1\right)^{2}} + \left(\frac{3 x^{2} \cos{\left(x \right)}}{x^{3} + 1} - \log{\left(x^{3} + 1 \right)} \sin{\left(x \right)}\right)^{3} - \frac{54 x^{3} \cos{\left(x \right)}}{\left(x^{3} + 1\right)^{2}} - \frac{9 x^{2} \cos{\left(x \right)}}{x^{3} + 1} - 3 \cdot \left(\frac{3 x^{2} \cos{\left(x \right)}}{x^{3} + 1} - \log{\left(x^{3} + 1 \right)} \sin{\left(x \right)}\right) \left(\frac{9 x^{4} \cos{\left(x \right)}}{\left(x^{3} + 1\right)^{2}} + \frac{6 x^{2} \sin{\left(x \right)}}{x^{3} + 1} + \log{\left(x^{3} + 1 \right)} \cos{\left(x \right)} - \frac{6 x \cos{\left(x \right)}}{x^{3} + 1}\right) + \log{\left(x^{3} + 1 \right)} \sin{\left(x \right)} - \frac{18 x \sin{\left(x \right)}}{x^{3} + 1} + \frac{6 \cos{\left(x \right)}}{x^{3} + 1}\right)$$