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z^(2/(z+1))
Derivada de la función/ (z+1)/ z^(2/(z+1))

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

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

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Solución

Ha introducido [src] 
   2  
 -----
 z + 1
z
z2z+1z^{\frac{2}{z + 1}} 
z^(2/(z + 1))
Solución detallada

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

    Perola derivada

    (2z+1)2z+1(log⁡(2z+1)+1)\left(\frac{2}{z + 1}\right)^{\frac{2}{z + 1}} \left(\log{\left(\frac{2}{z + 1} \right)} + 1\right)

  2. Simplificamos:

    (2z+1)2z+1(log⁡(2z+1)+1)\left(\frac{2}{z + 1}\right)^{\frac{2}{z + 1}} \left(\log{\left(\frac{2}{z + 1} \right)} + 1\right)

Respuesta:

(2z+1)2z+1(log⁡(2z+1)+1)\left(\frac{2}{z + 1}\right)^{\frac{2}{z + 1}} \left(\log{\left(\frac{2}{z + 1} \right)} + 1\right)

Gráfica
02468-8-6-4-2-10102-2
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Trazar el gráfico f'(x)
Primera derivada [src] 
   2                           
 -----                         
 z + 1 /  2*log(z)       2    \
z     *|- -------- + ---------|
       |         2   z*(z + 1)|
       \  (z + 1)             /
z2z+1(−2log⁡(z)(z+1)2+2z(z+1))z^{\frac{2}{z + 1}} \left(- \frac{2 \log{\left(z \right)}}{\left(z + 1\right)^{2}} + \frac{2}{z \left(z + 1\right)}\right)
Simplificar
Segunda derivada [src] 
         /                                   2           \
     2   |                     /  1   log(z)\            |
   ----- |                   2*|- - + ------|            |
   1 + z |  1        2         \  z   1 + z /    2*log(z)|
2*z     *|- -- - --------- + ----------------- + --------|
         |   2   z*(1 + z)         1 + z                2|
         \  z                                    (1 + z) /
----------------------------------------------------------
                          1 + z
2z2z+1(2(log⁡(z)z+1−1z)2z+1+2log⁡(z)(z+1)2−2z(z+1)−1z2)z+1\frac{2 z^{\frac{2}{z + 1}} \left(\frac{2 \left(\frac{\log{\left(z \right)}}{z + 1} - \frac{1}{z}\right)^{2}}{z + 1} + \frac{2 \log{\left(z \right)}}{\left(z + 1\right)^{2}} - \frac{2}{z \left(z + 1\right)} - \frac{1}{z^{2}}\right)}{z + 1}
Simplificar
Tercera derivada [src] 
         /                                3                               /  1   log(z)\ /1    2*log(z)       2    \\
     2   |                  /  1   log(z)\                              6*|- - + ------|*|-- - -------- + ---------||
   ----- |                4*|- - + ------|                                \  z   1 + z / | 2          2   z*(1 + z)||
   1 + z |2    6*log(z)     \  z   1 + z /        3            6                         \z    (1 + z)             /|
2*z     *|-- - -------- - ----------------- + ---------- + ---------- + --------------------------------------------|
         | 3          3               2        2                    2                      1 + z                    |
         \z    (1 + z)         (1 + z)        z *(1 + z)   z*(1 + z)                                                /
---------------------------------------------------------------------------------------------------------------------
                                                        1 + z
2z2z+1(6(log⁡(z)z+1−1z)(−2log⁡(z)(z+1)2+2z(z+1)+1z2)z+1−4(log⁡(z)z+1−1z)3(z+1)2−6log⁡(z)(z+1)3+6z(z+1)2+3z2(z+1)+2z3)z+1\frac{2 z^{\frac{2}{z + 1}} \left(\frac{6 \left(\frac{\log{\left(z \right)}}{z + 1} - \frac{1}{z}\right) \left(- \frac{2 \log{\left(z \right)}}{\left(z + 1\right)^{2}} + \frac{2}{z \left(z + 1\right)} + \frac{1}{z^{2}}\right)}{z + 1} - \frac{4 \left(\frac{\log{\left(z \right)}}{z + 1} - \frac{1}{z}\right)^{3}}{\left(z + 1\right)^{2}} - \frac{6 \log{\left(z \right)}}{\left(z + 1\right)^{3}} + \frac{6}{z \left(z + 1\right)^{2}} + \frac{3}{z^{2} \left(z + 1\right)} + \frac{2}{z^{3}}\right)}{z + 1}
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Gráfico
Derivada de z^(2/(z+1))
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