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