Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
cos(x) /cos(x) \
(x - 5) *|------ - log(x - 5)*sin(x)|
\x - 5 /
$$\left(x - 5\right)^{\cos{\left(x \right)}} \left(- \log{\left(x - 5 \right)} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x - 5}\right)$$
/ 2 \
cos(x) |/ cos(x)\ cos(x) 2*sin(x)|
(-5 + x) *||log(-5 + x)*sin(x) - ------| - --------- - cos(x)*log(-5 + x) - --------|
|\ -5 + x/ 2 -5 + x |
\ (-5 + x) /
$$\left(x - 5\right)^{\cos{\left(x \right)}} \left(\left(\log{\left(x - 5 \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x - 5}\right)^{2} - \log{\left(x - 5 \right)} \cos{\left(x \right)} - \frac{2 \sin{\left(x \right)}}{x - 5} - \frac{\cos{\left(x \right)}}{\left(x - 5\right)^{2}}\right)$$
/ 3 \
cos(x) | / cos(x)\ 3*cos(x) 2*cos(x) 3*sin(x) / cos(x)\ / cos(x) 2*sin(x)\|
(-5 + x) *|- |log(-5 + x)*sin(x) - ------| + log(-5 + x)*sin(x) - -------- + --------- + --------- + 3*|log(-5 + x)*sin(x) - ------|*|--------- + cos(x)*log(-5 + x) + --------||
| \ -5 + x/ -5 + x 3 2 \ -5 + x/ | 2 -5 + x ||
\ (-5 + x) (-5 + x) \(-5 + x) //
$$\left(x - 5\right)^{\cos{\left(x \right)}} \left(- \left(\log{\left(x - 5 \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x - 5}\right)^{3} + 3 \left(\log{\left(x - 5 \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x - 5}\right) \left(\log{\left(x - 5 \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x - 5} + \frac{\cos{\left(x \right)}}{\left(x - 5\right)^{2}}\right) + \log{\left(x - 5 \right)} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{x - 5} + \frac{3 \sin{\left(x \right)}}{\left(x - 5\right)^{2}} + \frac{2 \cos{\left(x \right)}}{\left(x - 5\right)^{3}}\right)$$