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Derivada de la función/ x^2^x

Derivada de x^2^x

Función f() - derivada -er orden en el punto
v

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Solución

Ha introducido [src] 
 / x\
 \2 /
x
$$x^{2^{x}}$$ 
x^(2^x)
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

  2. Simplificamos:

Respuesta:

Primera derivada [src] 
 / x\ / x                   \
 \2 / |2     x              |
x    *|-- + 2 *log(2)*log(x)|
      \x                    /
$$x^{2^{x}} \left(2^{x} \log{\left(2 \right)} \log{\left(x \right)} + \frac{2^{x}}{x}\right)$$
Simplificar
Segunda derivada [src] 
    / x\ /                             2                            \
 x  \2 / |  1     x /1                \       2             2*log(2)|
2 *x    *|- -- + 2 *|- + log(2)*log(x)|  + log (2)*log(x) + --------|
         |   2      \x                /                        x    |
         \  x                                                       /
$$2^{x} x^{2^{x}} \left(2^{x} \left(\log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \log{\left(2 \right)}^{2} \log{\left(x \right)} + \frac{2 \log{\left(2 \right)}}{x} - \frac{1}{x^{2}}\right)$$
Simplificar
Tercera derivada [src] 
    / x\ /                             3                                    2                                                                 \
 x  \2 / |2     2*x /1                \       3             3*log(2)   3*log (2)      x /1                \ /  1       2             2*log(2)\|
2 *x    *|-- + 2   *|- + log(2)*log(x)|  + log (2)*log(x) - -------- + --------- + 3*2 *|- + log(2)*log(x)|*|- -- + log (2)*log(x) + --------||
         | 3        \x                /                         2          x            \x                / |   2                       x    ||
         \x                                                    x                                            \  x                             //
$$2^{x} x^{2^{x}} \left(2^{2 x} \left(\log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 \cdot 2^{x} \left(\log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(2 \right)}^{2} \log{\left(x \right)} + \frac{2 \log{\left(2 \right)}}{x} - \frac{1}{x^{2}}\right) + \log{\left(2 \right)}^{3} \log{\left(x \right)} + \frac{3 \log{\left(2 \right)}^{2}}{x} - \frac{3 \log{\left(2 \right)}}{x^{2}} + \frac{2}{x^{3}}\right)$$
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