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x^(x*arctg(7x))

Derivada de x^(x*arctg(7x))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src]
 x*atan(7*x)
x           
$$x^{x \operatorname{atan}{\left(7 x \right)}}$$
x^(x*atan(7*x))
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
 x*atan(7*x) //   7*x               \                   \
x           *||--------- + atan(7*x)|*log(x) + atan(7*x)|
             ||        2            |                   |
             \\1 + 49*x             /                   /
$$x^{x \operatorname{atan}{\left(7 x \right)}} \left(\left(\frac{7 x}{49 x^{2} + 1} + \operatorname{atan}{\left(7 x \right)}\right) \log{\left(x \right)} + \operatorname{atan}{\left(7 x \right)}\right)$$
Segunda derivada [src]
             /                                                                                       /           2  \       \
             |                                                               7*x                     |       49*x   |       |
             |                                                            --------- + atan(7*x)   14*|-1 + ---------|*log(x)|
             |                                            2                       2                  |             2|       |
 x*atan(7*x) |//   7*x               \                   \        7       1 + 49*x                   \     1 + 49*x /       |
x           *|||--------- + atan(7*x)|*log(x) + atan(7*x)|  + --------- + --------------------- - --------------------------|
             |||        2            |                   |            2             x                             2         |
             \\\1 + 49*x             /                   /    1 + 49*x                                    1 + 49*x          /
$$x^{x \operatorname{atan}{\left(7 x \right)}} \left(\left(\left(\frac{7 x}{49 x^{2} + 1} + \operatorname{atan}{\left(7 x \right)}\right) \log{\left(x \right)} + \operatorname{atan}{\left(7 x \right)}\right)^{2} - \frac{14 \left(\frac{49 x^{2}}{49 x^{2} + 1} - 1\right) \log{\left(x \right)}}{49 x^{2} + 1} + \frac{7}{49 x^{2} + 1} + \frac{\frac{7 x}{49 x^{2} + 1} + \operatorname{atan}{\left(7 x \right)}}{x}\right)$$
Tercera derivada [src]
             /                                                                                                                                      /                                       /           2  \       \      /           2  \          /           2  \       \
             |                                                   7*x                                                                                |               7*x                     |       49*x   |       |      |       49*x   |          |       49*x   |       |
             |                                                --------- + atan(7*x)                                                                 |            --------- + atan(7*x)   14*|-1 + ---------|*log(x)|   28*|-1 + ---------|   2744*x*|-1 + ---------|*log(x)|
             |                                            3           2                                                                             |                    2                  |             2|       |      |             2|          |             2|       |
 x*atan(7*x) |//   7*x               \                   \    1 + 49*x                   686*x         //   7*x               \                   \ |    7       1 + 49*x                   \     1 + 49*x /       |      \     1 + 49*x /          \     1 + 49*x /       |
x           *|||--------- + atan(7*x)|*log(x) + atan(7*x)|  - --------------------- - ------------ + 3*||--------- + atan(7*x)|*log(x) + atan(7*x)|*|--------- + --------------------- - --------------------------| - ------------------- + ------------------------------|
             |||        2            |                   |               2                       2     ||        2            |                   | |        2             x                             2         |        /        2\                          2         |
             |\\1 + 49*x             /                   /              x             /        2\      \\1 + 49*x             /                   / \1 + 49*x                                    1 + 49*x          /      x*\1 + 49*x /               /        2\          |
             \                                                                        \1 + 49*x /                                                                                                                                                     \1 + 49*x /          /
$$x^{x \operatorname{atan}{\left(7 x \right)}} \left(\frac{2744 x \left(\frac{49 x^{2}}{49 x^{2} + 1} - 1\right) \log{\left(x \right)}}{\left(49 x^{2} + 1\right)^{2}} - \frac{686 x}{\left(49 x^{2} + 1\right)^{2}} + \left(\left(\frac{7 x}{49 x^{2} + 1} + \operatorname{atan}{\left(7 x \right)}\right) \log{\left(x \right)} + \operatorname{atan}{\left(7 x \right)}\right)^{3} + 3 \left(\left(\frac{7 x}{49 x^{2} + 1} + \operatorname{atan}{\left(7 x \right)}\right) \log{\left(x \right)} + \operatorname{atan}{\left(7 x \right)}\right) \left(- \frac{14 \left(\frac{49 x^{2}}{49 x^{2} + 1} - 1\right) \log{\left(x \right)}}{49 x^{2} + 1} + \frac{7}{49 x^{2} + 1} + \frac{\frac{7 x}{49 x^{2} + 1} + \operatorname{atan}{\left(7 x \right)}}{x}\right) - \frac{28 \left(\frac{49 x^{2}}{49 x^{2} + 1} - 1\right)}{x \left(49 x^{2} + 1\right)} - \frac{\frac{7 x}{49 x^{2} + 1} + \operatorname{atan}{\left(7 x \right)}}{x^{2}}\right)$$
Gráfico
Derivada de x^(x*arctg(7x))