Derivada de y=e^lnx^x

Ha introducido [src]

    x   
 log (x)
E

$$e^{\log{\left(x \right)}^{x}}$$

E^(log(x)^x)

Solución detallada

Sustituimos $u = \log{\left(x \right)}^{x}$ .
Derivado $e^{u}$ es.
Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \log{\left(x \right)}^{x}$ :
1. No logro encontrar los pasos en la búsqueda de esta derivada.
  
  Perola derivada
  
  $x^{x} \left(\log{\left(x \right)} + 1\right)$
Como resultado de la secuencia de reglas:

$x^{x} \left(\log{\left(x \right)} + 1\right) e^{\log{\left(x \right)}^{x}}$

Respuesta:

$x^{x} \left(\log{\left(x \right)} + 1\right) e^{\log{\left(x \right)}^{x}}$

Primera derivada [src]

                                   x   
   x    /  1                 \  log (x)
log (x)*|------ + log(log(x))|*e       
        \log(x)              /

$$\left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) e^{\log{\left(x \right)}^{x}} \log{\left(x \right)}^{x}$$

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Segunda derivada [src]

        /                                                                  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) /

$$\left(\left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} \log{\left(x \right)}^{x} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} + \frac{1 - \frac{1}{\log{\left(x \right)}}}{x \log{\left(x \right)}}\right) e^{\log{\left(x \right)}^{x}} \log{\left(x \right)}^{x}$$

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Tercera derivada [src]

        /                                                                                                         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)                                                                                         /

$$\left(\left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{3} \log{\left(x \right)}^{2 x} + 3 \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{3} \log{\left(x \right)}^{x} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{3} + \frac{3 \left(1 - \frac{1}{\log{\left(x \right)}}\right) \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}}{x \log{\left(x \right)}} + \frac{3 \left(1 - \frac{1}{\log{\left(x \right)}}\right) \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)}{x \log{\left(x \right)}} - \frac{1 - \frac{2}{\log{\left(x \right)}^{2}}}{x^{2} \log{\left(x \right)}}\right) e^{\log{\left(x \right)}^{x}} \log{\left(x \right)}^{x}$$

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Derivada de y=e^lnx^x

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