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y=(x+x^2)^x

Derivada de y=(x+x^2)^x

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

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

    Perola derivada


Respuesta:

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