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Derivada de la función/ log(x)/ (log(x))^(3^x)

Derivada de (log(x))^(3^x)

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

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Solución

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