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