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(x+x^3)^x

Derivada de (x+x^3)^x

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

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Solución

Ha introducido [src]
        x
/     3\ 
\x + x / 
$$\left(x^{3} + x\right)^{x}$$
(x + x^3)^x
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
        x /  /       2\              \
/     3\  |x*\1 + 3*x /      /     3\|
\x + x / *|------------ + log\x + x /|
          |        3                 |
          \   x + x                  /
$$\left(x^{3} + x\right)^{x} \left(\frac{x \left(3 x^{2} + 1\right)}{x^{3} + x} + \log{\left(x^{3} + x \right)}\right)$$
Segunda derivada [src]
              /                                                               2\
              |                                        /       2\   /       2\ |
              |                                      2*\1 + 3*x /   \1 + 3*x / |
              |                            2   6*x + ------------ - -----------|
            x |/       2                  \               x            /     2\|
/  /     2\\  ||1 + 3*x       /  /     2\\|                          x*\1 + x /|
\x*\1 + x // *||-------- + log\x*\1 + x //|  + --------------------------------|
              ||      2                   |                      2             |
              \\ 1 + x                    /                 1 + x              /
$$\left(x \left(x^{2} + 1\right)\right)^{x} \left(\left(\log{\left(x \left(x^{2} + 1\right) \right)} + \frac{3 x^{2} + 1}{x^{2} + 1}\right)^{2} + \frac{6 x + \frac{2 \left(3 x^{2} + 1\right)}{x} - \frac{\left(3 x^{2} + 1\right)^{2}}{x \left(x^{2} + 1\right)}}{x^{2} + 1}\right)$$
Tercera derivada [src]
              /                                                                  3               2                                                                    \
              |                                         /       2\     /       2\      /       2\                                   /                               2\|
              |                                      18*\1 + 3*x /   2*\1 + 3*x /    3*\1 + 3*x /      /       2                  \ |        /       2\   /       2\ ||
              |                                -24 + ------------- - ------------- + -------------     |1 + 3*x       /  /     2\\| |      2*\1 + 3*x /   \1 + 3*x / ||
              |                            3                  2                  2     2 /     2\    3*|-------- + log\x*\1 + x //|*|6*x + ------------ - -----------||
            x |/       2                  \              1 + x         2 /     2\     x *\1 + x /      |      2                   | |           x            /     2\||
/  /     2\\  ||1 + 3*x       /  /     2\\|                           x *\1 + x /                      \ 1 + x                    / \                      x*\1 + x //|
\x*\1 + x // *||-------- + log\x*\1 + x //|  - --------------------------------------------------- + -----------------------------------------------------------------|
              ||      2                   |                                2                                                            2                             |
              \\ 1 + x                    /                           1 + x                                                        1 + x                              /
$$\left(x \left(x^{2} + 1\right)\right)^{x} \left(\left(\log{\left(x \left(x^{2} + 1\right) \right)} + \frac{3 x^{2} + 1}{x^{2} + 1}\right)^{3} + \frac{3 \left(\log{\left(x \left(x^{2} + 1\right) \right)} + \frac{3 x^{2} + 1}{x^{2} + 1}\right) \left(6 x + \frac{2 \left(3 x^{2} + 1\right)}{x} - \frac{\left(3 x^{2} + 1\right)^{2}}{x \left(x^{2} + 1\right)}\right)}{x^{2} + 1} - \frac{-24 + \frac{18 \left(3 x^{2} + 1\right)}{x^{2} + 1} + \frac{3 \left(3 x^{2} + 1\right)^{2}}{x^{2} \left(x^{2} + 1\right)} - \frac{2 \left(3 x^{2} + 1\right)^{3}}{x^{2} \left(x^{2} + 1\right)^{2}}}{x^{2} + 1}\right)$$
Gráfico
Derivada de (x+x^3)^x