Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
/ cos(x)\ / cos(x) \
\8 / |8 cos(x) |
x *|------- - 8 *log(8)*log(x)*sin(x)|
\ x /
$$x^{8^{\cos{\left(x \right)}}} \left(- 8^{\cos{\left(x \right)}} \log{\left(8 \right)} \log{\left(x \right)} \sin{\left(x \right)} + \frac{8^{\cos{\left(x \right)}}}{x}\right)$$
/ cos(x)\ / 2 \
cos(x) \8 / | 1 cos(x) / 1 \ 2 2 2*log(8)*sin(x)|
8 *x *|- -- + 8 *|- - + log(8)*log(x)*sin(x)| + log (8)*sin (x)*log(x) - cos(x)*log(8)*log(x) - ---------------|
| 2 \ x / x |
\ x /
$$8^{\cos{\left(x \right)}} x^{8^{\cos{\left(x \right)}}} \left(8^{\cos{\left(x \right)}} \left(\log{\left(8 \right)} \log{\left(x \right)} \sin{\left(x \right)} - \frac{1}{x}\right)^{2} + \log{\left(8 \right)}^{2} \log{\left(x \right)} \sin^{2}{\left(x \right)} - \log{\left(8 \right)} \log{\left(x \right)} \cos{\left(x \right)} - \frac{2 \log{\left(8 \right)} \sin{\left(x \right)}}{x} - \frac{1}{x^{2}}\right)$$
/ cos(x)\ / 3 2 2 \
cos(x) \8 / |2 2*cos(x) / 1 \ 3 3 3*cos(x)*log(8) cos(x) / 1 \ /1 2 2 2*log(8)*sin(x)\ 3*log (8)*sin (x) 3*log(8)*sin(x) 2 |
8 *x *|-- - 8 *|- - + log(8)*log(x)*sin(x)| + log(8)*log(x)*sin(x) - log (8)*sin (x)*log(x) - --------------- + 3*8 *|- - + log(8)*log(x)*sin(x)|*|-- + cos(x)*log(8)*log(x) - log (8)*sin (x)*log(x) + ---------------| + ----------------- + --------------- + 3*log (8)*cos(x)*log(x)*sin(x)|
| 3 \ x / x \ x / | 2 x | x 2 |
\x \x / x /
$$8^{\cos{\left(x \right)}} x^{8^{\cos{\left(x \right)}}} \left(- 8^{2 \cos{\left(x \right)}} \left(\log{\left(8 \right)} \log{\left(x \right)} \sin{\left(x \right)} - \frac{1}{x}\right)^{3} + 3 \cdot 8^{\cos{\left(x \right)}} \left(\log{\left(8 \right)} \log{\left(x \right)} \sin{\left(x \right)} - \frac{1}{x}\right) \left(- \log{\left(8 \right)}^{2} \log{\left(x \right)} \sin^{2}{\left(x \right)} + \log{\left(8 \right)} \log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \log{\left(8 \right)} \sin{\left(x \right)}}{x} + \frac{1}{x^{2}}\right) - \log{\left(8 \right)}^{3} \log{\left(x \right)} \sin^{3}{\left(x \right)} + 3 \log{\left(8 \right)}^{2} \log{\left(x \right)} \sin{\left(x \right)} \cos{\left(x \right)} + \log{\left(8 \right)} \log{\left(x \right)} \sin{\left(x \right)} + \frac{3 \log{\left(8 \right)}^{2} \sin^{2}{\left(x \right)}}{x} - \frac{3 \log{\left(8 \right)} \cos{\left(x \right)}}{x} + \frac{3 \log{\left(8 \right)} \sin{\left(x \right)}}{x^{2}} + \frac{2}{x^{3}}\right)$$