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