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(x+1)^(2/x)

Derivada de (x+1)^(2/x)

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

Gráfico:

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Solución

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

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
       2                             
       -                             
       x /  2*log(x + 1)       2    \
(x + 1) *|- ------------ + ---------|
         |        2        x*(x + 1)|
         \       x                  /
$$\left(x + 1\right)^{\frac{2}{x}} \left(\frac{2}{x \left(x + 1\right)} - \frac{2 \log{\left(x + 1 \right)}}{x^{2}}\right)$$
Segunda derivada [src]
           /                                               2               \
         2 |                           /  1     log(1 + x)\                |
         - |                         2*|----- - ----------|                |
         x |     1           2         \1 + x       x     /    2*log(1 + x)|
2*(1 + x) *|- -------- - --------- + ----------------------- + ------------|
           |         2   x*(1 + x)              x                    2     |
           \  (1 + x)                                               x      /
----------------------------------------------------------------------------
                                     x                                      
$$\frac{2 \left(x + 1\right)^{\frac{2}{x}} \left(- \frac{1}{\left(x + 1\right)^{2}} + \frac{2 \left(\frac{1}{x + 1} - \frac{\log{\left(x + 1 \right)}}{x}\right)^{2}}{x} - \frac{2}{x \left(x + 1\right)} + \frac{2 \log{\left(x + 1 \right)}}{x^{2}}\right)}{x}$$
Tercera derivada [src]
           /                                                             3                  /  1     log(1 + x)\ /   1       2*log(1 + x)       2    \\
         2 |                                         /  1     log(1 + x)\                 6*|----- - ----------|*|-------- - ------------ + ---------||
         - |                                       4*|----- - ----------|                   \1 + x       x     / |       2         2        x*(1 + x)||
         x |   2       6*log(1 + x)       3          \1 + x       x     /        6                               \(1 + x)         x                  /|
2*(1 + x) *|-------- - ------------ + ---------- + ----------------------- + ---------- - ------------------------------------------------------------|
           |       3         3                 2               2              2                                        x                              |
           \(1 + x)         x         x*(1 + x)               x              x *(1 + x)                                                               /
-------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                           x                                                                           
$$\frac{2 \left(x + 1\right)^{\frac{2}{x}} \left(\frac{2}{\left(x + 1\right)^{3}} - \frac{6 \left(\frac{1}{x + 1} - \frac{\log{\left(x + 1 \right)}}{x}\right) \left(\frac{1}{\left(x + 1\right)^{2}} + \frac{2}{x \left(x + 1\right)} - \frac{2 \log{\left(x + 1 \right)}}{x^{2}}\right)}{x} + \frac{3}{x \left(x + 1\right)^{2}} + \frac{4 \left(\frac{1}{x + 1} - \frac{\log{\left(x + 1 \right)}}{x}\right)^{3}}{x^{2}} + \frac{6}{x^{2} \left(x + 1\right)} - \frac{6 \log{\left(x + 1 \right)}}{x^{3}}\right)}{x}$$
Gráfico
Derivada de (x+1)^(2/x)