Solución detallada
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Sustituimos .
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Derivado es.
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Luego se aplica una cadena de reglas. Multiplicamos por :
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Como resultado de la secuencia de reglas:
Respuesta:
x
x / 1 \ log (x)
log (x)*|------ + log(log(x))|*e
\log(x) /
$$\left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) e^{\log{\left(x \right)}^{x}} \log{\left(x \right)}^{x}$$
/ 1 \
| 2 2 1 - ------| x
x |/ 1 \ / 1 \ x log(x)| log (x)
log (x)*||------ + log(log(x))| + |------ + log(log(x))| *log (x) + ----------|*e
\\log(x) / \log(x) / x*log(x) /
$$\left(\left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} \log{\left(x \right)}^{x} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} + \frac{1 - \frac{1}{\log{\left(x \right)}}}{x \log{\left(x \right)}}\right) e^{\log{\left(x \right)}^{x}} \log{\left(x \right)}^{x}$$
/ 2 \
| 1 - ------- / 1 \ / 1 \ x / 1 \ / 1 \|
| 3 3 3 2 3*|1 - ------|*|------ + log(log(x))| 3*log (x)*|1 - ------|*|------ + log(log(x))|| x
x |/ 1 \ / 1 \ 2*x / 1 \ x log (x) \ log(x)/ \log(x) / \ log(x)/ \log(x) /| log (x)
log (x)*||------ + log(log(x))| + |------ + log(log(x))| *log (x) + 3*|------ + log(log(x))| *log (x) - ----------- + ------------------------------------- + ---------------------------------------------|*e
|\log(x) / \log(x) / \log(x) / 2 x*log(x) x*log(x) |
\ x *log(x) /
$$\left(\left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{3} \log{\left(x \right)}^{2 x} + 3 \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{3} \log{\left(x \right)}^{x} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{3} + \frac{3 \left(1 - \frac{1}{\log{\left(x \right)}}\right) \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}}{x \log{\left(x \right)}} + \frac{3 \left(1 - \frac{1}{\log{\left(x \right)}}\right) \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)}{x \log{\left(x \right)}} - \frac{1 - \frac{2}{\log{\left(x \right)}^{2}}}{x^{2} \log{\left(x \right)}}\right) e^{\log{\left(x \right)}^{x}} \log{\left(x \right)}^{x}$$