Sr Examen

Derivada de (x^exp)^tg(x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

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

    Perola derivada


Respuesta:

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