Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
cos(x) /cos(x) \
(1 + x) *|------ - log(1 + x)*sin(x)|
\1 + x /
$$\left(x + 1\right)^{\cos{\left(x \right)}} \left(- \log{\left(x + 1 \right)} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x + 1}\right)$$
/ 2 \
cos(x) |/ cos(x)\ cos(x) 2*sin(x)|
(1 + x) *||log(1 + x)*sin(x) - ------| - -------- - cos(x)*log(1 + x) - --------|
|\ 1 + x / 2 1 + x |
\ (1 + x) /
$$\left(x + 1\right)^{\cos{\left(x \right)}} \left(\left(\log{\left(x + 1 \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x + 1}\right)^{2} - \log{\left(x + 1 \right)} \cos{\left(x \right)} - \frac{2 \sin{\left(x \right)}}{x + 1} - \frac{\cos{\left(x \right)}}{\left(x + 1\right)^{2}}\right)$$
/ 3 \
cos(x) | / cos(x)\ 3*cos(x) 2*cos(x) 3*sin(x) / cos(x)\ / cos(x) 2*sin(x)\|
(1 + x) *|- |log(1 + x)*sin(x) - ------| + log(1 + x)*sin(x) - -------- + -------- + -------- + 3*|log(1 + x)*sin(x) - ------|*|-------- + cos(x)*log(1 + x) + --------||
| \ 1 + x / 1 + x 3 2 \ 1 + x / | 2 1 + x ||
\ (1 + x) (1 + x) \(1 + x) //
$$\left(x + 1\right)^{\cos{\left(x \right)}} \left(- \left(\log{\left(x + 1 \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x + 1}\right)^{3} + 3 \left(\log{\left(x + 1 \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x + 1}\right) \left(\log{\left(x + 1 \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x + 1} + \frac{\cos{\left(x \right)}}{\left(x + 1\right)^{2}}\right) + \log{\left(x + 1 \right)} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{x + 1} + \frac{3 \sin{\left(x \right)}}{\left(x + 1\right)^{2}} + \frac{2 \cos{\left(x \right)}}{\left(x + 1\right)^{3}}\right)$$