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x^(1/x^2)

Derivada de x^(1/x^2)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src]
 1 
 --
  2
 x 
x  
x1x2x^{\frac{1}{x^{2}}}
x^(1/(x^2))
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log(1x2)+1)x2x2\left(\log{\left(\frac{1}{x^{2}} \right)} + 1\right) \left|{x}\right|^{- \frac{2}{x^{2}}}

  2. Simplificamos:

    (log(1x2)+1)x2x2\left(\log{\left(\frac{1}{x^{2}} \right)} + 1\right) \left|{x}\right|^{- \frac{2}{x^{2}}}


Respuesta:

(log(1x2)+1)x2x2\left(\log{\left(\frac{1}{x^{2}} \right)} + 1\right) \left|{x}\right|^{- \frac{2}{x^{2}}}

Gráfica
02468-8-6-4-2-10102.5-2.5
Primera derivada [src]
 1                   
 --                  
  2                  
 x  / 1     2*log(x)\
x  *|---- - --------|
    |   2       3   |
    \x*x       x    /
x1x2(1xx22log(x)x3)x^{\frac{1}{x^{2}}} \left(\frac{1}{x x^{2}} - \frac{2 \log{\left(x \right)}}{x^{3}}\right)
Segunda derivada [src]
 1                                   
 --                                  
  2 /                              2\
 x  |                (1 - 2*log(x)) |
x  *|-5 + 6*log(x) + ---------------|
    |                        2      |
    \                       x       /
-------------------------------------
                   4                 
                  x                  
x1x2(6log(x)5+(12log(x))2x2)x4\frac{x^{\frac{1}{x^{2}}} \left(6 \log{\left(x \right)} - 5 + \frac{\left(1 - 2 \log{\left(x \right)}\right)^{2}}{x^{2}}\right)}{x^{4}}
Tercera derivada [src]
 1                                                                       
 --                                                                      
  2 /                               3                                   \
 x  |                 (1 - 2*log(x))    3*(1 - 2*log(x))*(-5 + 6*log(x))|
x  *|26 - 24*log(x) + --------------- + --------------------------------|
    |                         4                         2               |
    \                        x                         x                /
-------------------------------------------------------------------------
                                     5                                   
                                    x                                    
x1x2(24log(x)+26+3(12log(x))(6log(x)5)x2+(12log(x))3x4)x5\frac{x^{\frac{1}{x^{2}}} \left(- 24 \log{\left(x \right)} + 26 + \frac{3 \left(1 - 2 \log{\left(x \right)}\right) \left(6 \log{\left(x \right)} - 5\right)}{x^{2}} + \frac{\left(1 - 2 \log{\left(x \right)}\right)^{3}}{x^{4}}\right)}{x^{5}}
Gráfico
Derivada de x^(1/x^2)