Solución detallada
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diferenciamos miembro por miembro:
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diferenciamos miembro por miembro:
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Como resultado de:
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Sustituimos .
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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:
Como resultado de:
Respuesta:
/ x\ / x \ / a\ / a a \ / x\
\a / |a x | \x / |x a*x *log(x)| \x / x
x *|-- + a *log(a)*log(x)| + x *|-- + -----------| + a *x *(1 + log(x))*log(a)
\x / \x x /
$$a^{x^{x}} x^{x} \left(\log{\left(x \right)} + 1\right) \log{\left(a \right)} + x^{a^{x}} \left(a^{x} \log{\left(a \right)} \log{\left(x \right)} + \frac{a^{x}}{x}\right) + x^{x^{a}} \left(\frac{a x^{a} \log{\left(x \right)}}{x} + \frac{x^{a}}{x}\right)$$
/ x\ / a\ / a\
/ x\ / x\ 2 \x / x / x\ / x\ a \x / / 2 \ \x / 2*a 2
x \a / / 1 2 2*log(a)\ 2*x \a / /1 \ a *x *log(a) \x / x 2 \x / 2*x 2 2 x *x *\-1 + 2*a + a *log(x) - a*log(x)/ x *x *(1 + a*log(x))
a *x *|- -- + log (a)*log(x) + --------| + a *x *|- + log(a)*log(x)| + --------------- + a *x *(1 + log(x)) *log(a) + a *x *(1 + log(x)) *log (a) + ------------------------------------------ + --------------------------
| 2 x | \x / x 2 2
\ x / x x
$$a^{2 x} x^{a^{x}} \left(\log{\left(a \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{2} + a^{x} x^{a^{x}} \left(\log{\left(a \right)}^{2} \log{\left(x \right)} + \frac{2 \log{\left(a \right)}}{x} - \frac{1}{x^{2}}\right) + a^{x^{x}} x^{2 x} \left(\log{\left(x \right)} + 1\right)^{2} \log{\left(a \right)}^{2} + a^{x^{x}} x^{x} \left(\log{\left(x \right)} + 1\right)^{2} \log{\left(a \right)} + \frac{a^{x^{x}} x^{x} \log{\left(a \right)}}{x} + \frac{x^{2 a} x^{x^{a}} \left(a \log{\left(x \right)} + 1\right)^{2}}{x^{2}} + \frac{x^{a} x^{x^{a}} \left(a^{2} \log{\left(x \right)} - a \log{\left(x \right)} + 2 a - 1\right)}{x^{2}}$$
/ a\ / a\ / x\ / x\ / x\ / a\
/ x\ / 2 \ / x\ 3 / x\ / x\ a \x / / 2 3 2 \ \x / 3*a 3 \x / x / x\ / x\ \x / x \x / 2*x 2 \x / 2*a / 2 \
x \a / |2 3 3*log(a) 3*log (a)| 3*x \a / /1 \ \x / x 3 \x / 3*x 3 3 x *x *\2 - 6*a + 3*a + a *log(x) - 3*a *log(x) + 2*a*log(x)/ x *x *(1 + a*log(x)) a *x *log(a) \x / 2*x 3 2 2*x \a / /1 \ / 1 2 2*log(a)\ 3*a *x *(1 + log(x))*log(a) 3*a *x *log (a)*(1 + log(x)) 3*x *x *(1 + a*log(x))*\-1 + 2*a + a *log(x) - a*log(x)/
a *x *|-- + log (a)*log(x) - -------- + ---------| + a *x *|- + log(a)*log(x)| + a *x *(1 + log(x)) *log(a) + a *x *(1 + log(x)) *log (a) + ---------------------------------------------------------------- + -------------------------- - --------------- + 3*a *x *(1 + log(x)) *log (a) + 3*a *x *|- + log(a)*log(x)|*|- -- + log (a)*log(x) + --------| + ------------------------------ + --------------------------------- + -------------------------------------------------------------
| 3 2 x | \x / 3 3 2 \x / | 2 x | x x 3
\x x / x x x \ x / x
$$a^{3 x} x^{a^{x}} \left(\log{\left(a \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 a^{2 x} x^{a^{x}} \left(\log{\left(a \right)} \log{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(a \right)}^{2} \log{\left(x \right)} + \frac{2 \log{\left(a \right)}}{x} - \frac{1}{x^{2}}\right) + a^{x} x^{a^{x}} \left(\log{\left(a \right)}^{3} \log{\left(x \right)} + \frac{3 \log{\left(a \right)}^{2}}{x} - \frac{3 \log{\left(a \right)}}{x^{2}} + \frac{2}{x^{3}}\right) + a^{x^{x}} x^{3 x} \left(\log{\left(x \right)} + 1\right)^{3} \log{\left(a \right)}^{3} + 3 a^{x^{x}} x^{2 x} \left(\log{\left(x \right)} + 1\right)^{3} \log{\left(a \right)}^{2} + a^{x^{x}} x^{x} \left(\log{\left(x \right)} + 1\right)^{3} \log{\left(a \right)} + \frac{3 a^{x^{x}} x^{2 x} \left(\log{\left(x \right)} + 1\right) \log{\left(a \right)}^{2}}{x} + \frac{3 a^{x^{x}} x^{x} \left(\log{\left(x \right)} + 1\right) \log{\left(a \right)}}{x} - \frac{a^{x^{x}} x^{x} \log{\left(a \right)}}{x^{2}} + \frac{x^{3 a} x^{x^{a}} \left(a \log{\left(x \right)} + 1\right)^{3}}{x^{3}} + \frac{3 x^{2 a} x^{x^{a}} \left(a \log{\left(x \right)} + 1\right) \left(a^{2} \log{\left(x \right)} - a \log{\left(x \right)} + 2 a - 1\right)}{x^{3}} + \frac{x^{a} x^{x^{a}} \left(a^{3} \log{\left(x \right)} - 3 a^{2} \log{\left(x \right)} + 3 a^{2} + 2 a \log{\left(x \right)} - 6 a + 2\right)}{x^{3}}$$