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x^(x/(lnx*lnx))

Derivada de x^(x/(lnx*lnx))

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

Gráfico:

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Solución

Ha introducido [src]
       x      
 -------------
 log(x)*log(x)
x             
$$x^{\frac{x}{\log{\left(x \right)} \log{\left(x \right)}}}$$
x^(x/((log(x)*log(x))))
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

  2. Simplificamos:


Respuesta:

Gráfica
Primera derivada [src]
       x                                                   
 -------------                                             
 log(x)*log(x) /   1      /      1            2   \       \
x             *|------- + |------------- - -------|*log(x)|
               |   2      |log(x)*log(x)      3   |       |
               \log (x)   \                log (x)/       /
$$x^{\frac{x}{\log{\left(x \right)} \log{\left(x \right)}}} \left(\left(- \frac{2}{\log{\left(x \right)}^{3}} + \frac{1}{\log{\left(x \right)} \log{\left(x \right)}}\right) \log{\left(x \right)} + \frac{1}{\log{\left(x \right)}^{2}}\right)$$
Segunda derivada [src]
    x                                
 ------- /                      2   \
    2    |            2   1 - ------|
 log (x) |/      1   \        log(x)|
x       *||1 - ------|  - ----------|
         \\    log(x)/        x     /
-------------------------------------
                  2                  
               log (x)               
$$\frac{x^{\frac{x}{\log{\left(x \right)}^{2}}} \left(\left(1 - \frac{1}{\log{\left(x \right)}}\right)^{2} - \frac{1 - \frac{2}{\log{\left(x \right)}}}{x}\right)}{\log{\left(x \right)}^{2}}$$
Tercera derivada [src]
         /                         /      3   \                                              \
         |                       4*|1 - ------|                                              |
    x    |       18       4        \    log(x)/               3                              |
 ------- |1 - ------- + ------ - --------------   /      1   \      /      1   \ /      2   \|
    2    |       2      log(x)       log(x)       |1 - ------|    3*|1 - ------|*|1 - ------||
 log (x) |    log (x)                             \    log(x)/      \    log(x)/ \    log(x)/|
x       *|------------------------------------- + ------------- - ---------------------------|
         |                   2                        log(x)                x*log(x)         |
         \                  x                                                                /
----------------------------------------------------------------------------------------------
                                              2                                               
                                           log (x)                                            
$$\frac{x^{\frac{x}{\log{\left(x \right)}^{2}}} \left(\frac{\left(1 - \frac{1}{\log{\left(x \right)}}\right)^{3}}{\log{\left(x \right)}} - \frac{3 \left(1 - \frac{2}{\log{\left(x \right)}}\right) \left(1 - \frac{1}{\log{\left(x \right)}}\right)}{x \log{\left(x \right)}} + \frac{- \frac{4 \left(1 - \frac{3}{\log{\left(x \right)}}\right)}{\log{\left(x \right)}} + 1 + \frac{4}{\log{\left(x \right)}} - \frac{18}{\log{\left(x \right)}^{2}}}{x^{2}}\right)}{\log{\left(x \right)}^{2}}$$
Gráfico
Derivada de x^(x/(lnx*lnx))