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y=(lnx)^x^2
Derivada de la función/ y=(lnx)/ (lnx)^x/ y=(lnx)^x^2

Derivada de y=(lnx)^x^2

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

Gráfico:

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Definida a trozos:

Solución

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

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

    Perola derivada

Respuesta:

Gráfica
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        / 2\                           
        \x / /  x                     \
(log(x))    *|------ + 2*x*log(log(x))|
             \log(x)                  /
$$\left(2 x \log{\left(\log{\left(x \right)} \right)} + \frac{x}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x^{2}}$$
Simplificar
Segunda derivada [src] 
        / 2\ /                                                                2\
        \x / |     1                        3       2 /  1                   \ |
(log(x))    *|- ------- + 2*log(log(x)) + ------ + x *|------ + 2*log(log(x))| |
             |     2                      log(x)      \log(x)                / |
             \  log (x)                                                        /
$$\left(x^{2} \left(2 \log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} + 2 \log{\left(\log{\left(x \right)} \right)} + \frac{3}{\log{\left(x \right)}} - \frac{1}{\log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{x^{2}}$$
Simplificar
Tercera derivada [src] 
             /                                     3         2                                                                       \
             |                               2 - ------ + -------                                                                    |
        / 2\ |                           3       log(x)      2                                                                       |
        \x / | 3 /  1                   \                 log (x)       /  1                   \ /     1                        3   \|
(log(x))    *|x *|------ + 2*log(log(x))|  + -------------------- + 3*x*|------ + 2*log(log(x))|*|- ------- + 2*log(log(x)) + ------||
             |   \log(x)                /          x*log(x)             \log(x)                / |     2                      log(x)||
             \                                                                                   \  log (x)                         //
$$\left(x^{3} \left(2 \log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{3} + 3 x \left(2 \log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \left(2 \log{\left(\log{\left(x \right)} \right)} + \frac{3}{\log{\left(x \right)}} - \frac{1}{\log{\left(x \right)}^{2}}\right) + \frac{2 - \frac{3}{\log{\left(x \right)}} + \frac{2}{\log{\left(x \right)}^{2}}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{x^{2}}$$
Simplificar
Gráfico
Derivada de y=(lnx)^x^2
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