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(1+x)^(1/x)
Derivada de la función/ (1/x)/ (1+x)/ (1+x)^(1/x)

Derivada de (1+x)^(1/x)

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

Ha introducido [src] 
x _______
\/ 1 + x
(x+1)1x\left(x + 1\right)^{\frac{1}{x}} 
(1 + x)^(1/x)
Solución detallada

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-200200
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Trazar el gráfico f'(x)
Primera derivada [src] 
x _______ /    1       log(1 + x)\
\/ 1 + x *|--------- - ----------|
          |x*(1 + x)        2    |
          \                x     /
(x+1)1x(1x(x+1)−log⁡(x+1)x2)\left(x + 1\right)^{\frac{1}{x}} \left(\frac{1}{x \left(x + 1\right)} - \frac{\log{\left(x + 1 \right)}}{x^{2}}\right)
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Segunda derivada [src] 
          /                                 2                           \
          |             /  1     log(1 + x)\                            |
          |             |----- - ----------|                            |
x _______ |     1       \1 + x       x     /        2       2*log(1 + x)|
\/ 1 + x *|- -------- + --------------------- - --------- + ------------|
          |         2             x             x*(1 + x)         2     |
          \  (1 + x)                                             x      /
-------------------------------------------------------------------------
                                    x
(x+1)1x(−1(x+1)2+(1x+1−log⁡(x+1)x)2x−2x(x+1)+2log⁡(x+1)x2)x\frac{\left(x + 1\right)^{\frac{1}{x}} \left(- \frac{1}{\left(x + 1\right)^{2}} + \frac{\left(\frac{1}{x + 1} - \frac{\log{\left(x + 1 \right)}}{x}\right)^{2}}{x} - \frac{2}{x \left(x + 1\right)} + \frac{2 \log{\left(x + 1 \right)}}{x^{2}}\right)}{x}
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Tercera derivada [src] 
          /                               3                                              /  1     log(1 + x)\ /   1       2*log(1 + x)       2    \\
          |           /  1     log(1 + x)\                                             3*|----- - ----------|*|-------- - ------------ + ---------||
          |           |----- - ----------|                                               \1 + x       x     / |       2         2        x*(1 + x)||
x _______ |   2       \1 + x       x     /    6*log(1 + x)       3            6                               \(1 + x)         x                  /|
\/ 1 + x *|-------- + --------------------- - ------------ + ---------- + ---------- - ------------------------------------------------------------|
          |       3              2                  3                 2    2                                        x                              |
          \(1 + x)              x                  x         x*(1 + x)    x *(1 + x)                                                               /
----------------------------------------------------------------------------------------------------------------------------------------------------
                                                                         x
(x+1)1x(2(x+1)3−3(1x+1−log⁡(x+1)x)(1(x+1)2+2x(x+1)−2log⁡(x+1)x2)x+3x(x+1)2+(1x+1−log⁡(x+1)x)3x2+6x2(x+1)−6log⁡(x+1)x3)x\frac{\left(x + 1\right)^{\frac{1}{x}} \left(\frac{2}{\left(x + 1\right)^{3}} - \frac{3 \left(\frac{1}{x + 1} - \frac{\log{\left(x + 1 \right)}}{x}\right) \left(\frac{1}{\left(x + 1\right)^{2}} + \frac{2}{x \left(x + 1\right)} - \frac{2 \log{\left(x + 1 \right)}}{x^{2}}\right)}{x} + \frac{3}{x \left(x + 1\right)^{2}} + \frac{\left(\frac{1}{x + 1} - \frac{\log{\left(x + 1 \right)}}{x}\right)^{3}}{x^{2}} + \frac{6}{x^{2} \left(x + 1\right)} - \frac{6 \log{\left(x + 1 \right)}}{x^{3}}\right)}{x}
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Gráfico
Derivada de (1+x)^(1/x)
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