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Derivada de la función/ x^exp/ x^exp(x^exp(1))

Derivada de x^exp(x^exp(1))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
 / / / 1\\\
 | | \e /||
 | \x    /|
 \e       /
x
xexe1x^{e^{x^{e^{1}}}} 
x^exp(x^exp(1))
Solución detallada

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

    Perola derivada

    (log⁡(exe1)+1)(exe1)exe1\left(\log{\left(e^{x^{e^{1}}} \right)} + 1\right) \left(e^{x^{e^{1}}}\right)^{e^{x^{e^{1}}}}

  2. Simplificamos:

    (log⁡(exe)+1)(exe)exe\left(\log{\left(e^{x^{e}} \right)} + 1\right) \left(e^{x^{e}}\right)^{e^{x^{e}}}

Respuesta:

(log⁡(exe)+1)(exe)exe\left(\log{\left(e^{x^{e}} \right)} + 1\right) \left(e^{x^{e}}\right)^{e^{x^{e}}}

Primera derivada [src] 
 / / / 1\\\ / / / 1\\            / / 1\\       \
 | | \e /|| | | \e /|      / 1\  | \e /|       |
 | \x    /| | \x    /      \e /  \x    /       |
 \e       / |e          E*x    *e       *log(x)|
x          *|-------- + -----------------------|
            \   x                  x           /
xexe1(exe1exe1log⁡(x)x+exe1x)x^{e^{x^{e^{1}}}} \left(\frac{e x^{e^{1}} e^{x^{e^{1}}} \log{\left(x \right)}}{x} + \frac{e^{x^{e^{1}}}}{x}\right)
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Segunda derivada [src] 
 / / / 1\\\                                                                                                               
 | | \e /|| /                         2  / / 1\\                                                                \  / / 1\\
 | \x    /| |     /       / 1\       \   | \e /|        / 1\                     / 1\                / 1\       |  | \e /|
 \e       / |     |       \e /       |   \x    /        \e /    2*E  2           \e /  2             \e /       |  \x    /
x          *\-1 + \1 + E*x    *log(x)/ *e        + 2*E*x     + x   *e *log(x) + x    *e *log(x) - E*x    *log(x)/*e       
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                                                             2                                                            
                                                            x
xexe1(x2ee2log⁡(x)−exe1log⁡(x)+xe1e2log⁡(x)+2exe1+(exe1log⁡(x)+1)2exe1−1)exe1x2\frac{x^{e^{x^{e^{1}}}} \left(x^{2 e} e^{2} \log{\left(x \right)} - e x^{e^{1}} \log{\left(x \right)} + x^{e^{1}} e^{2} \log{\left(x \right)} + 2 e x^{e^{1}} + \left(e x^{e^{1}} \log{\left(x \right)} + 1\right)^{2} e^{x^{e^{1}}} - 1\right) e^{x^{e^{1}}}}{x^{2}}
Simplificar
Tercera derivada [src] 
 / / / 1\\\                                                                                                                                                                                                                                                                                                                
 | | \e /|| /                        3     / 1\                                                                                                                                                                                                                                    / / 1\\                       \  / / 1\\
 | \x    /| |    /       / 1\       \      \e /        / 1\                  / 1\       / 1\                                   / 1\                  / 1\                               /       / 1\       \ /          / 1\                     / 1\                / 1\       \  | \e /|         / 1\          |  | \e /|
 \e       / |    |       \e /       |   2*x            \e /      2*E  2      \e /  2    \e /  3             2*E  2             \e /  2               \e /             2*E  3            |       \e /       | |          \e /    2*E  2           \e /  2             \e /       |  \x    /    2*E  \e /  3       |  \x    /
x          *\2 + \1 + E*x    *log(x)/ *e        - 6*E*x     + 3*x   *e  + 3*x    *e  + x    *e *log(x) - 3*x   *e *log(x) - 3*x    *e *log(x) + 2*E*x    *log(x) + 3*x   *e *log(x) + 3*\1 + E*x    *log(x)/*\-1 + 2*E*x     + x   *e *log(x) + x    *e *log(x) - E*x    *log(x)/*e        + x   *x    *e *log(x)/*e       
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                                                                                                                                                              3                                                                                                                                                            
                                                                                                                                                             x
xexe1(x2exe1e3log⁡(x)−3x2ee2log⁡(x)+3x2ee3log⁡(x)+3x2ee2−3xe1e2log⁡(x)+2exe1log⁡(x)+xe1e3log⁡(x)−6exe1+3xe1e2+(exe1log⁡(x)+1)3e2xe1+3(exe1log⁡(x)+1)(x2ee2log⁡(x)−exe1log⁡(x)+xe1e2log⁡(x)+2exe1−1)exe1+2)exe1x3\frac{x^{e^{x^{e^{1}}}} \left(x^{2 e} x^{e^{1}} e^{3} \log{\left(x \right)} - 3 x^{2 e} e^{2} \log{\left(x \right)} + 3 x^{2 e} e^{3} \log{\left(x \right)} + 3 x^{2 e} e^{2} - 3 x^{e^{1}} e^{2} \log{\left(x \right)} + 2 e x^{e^{1}} \log{\left(x \right)} + x^{e^{1}} e^{3} \log{\left(x \right)} - 6 e x^{e^{1}} + 3 x^{e^{1}} e^{2} + \left(e x^{e^{1}} \log{\left(x \right)} + 1\right)^{3} e^{2 x^{e^{1}}} + 3 \left(e x^{e^{1}} \log{\left(x \right)} + 1\right) \left(x^{2 e} e^{2} \log{\left(x \right)} - e x^{e^{1}} \log{\left(x \right)} + x^{e^{1}} e^{2} \log{\left(x \right)} + 2 e x^{e^{1}} - 1\right) e^{x^{e^{1}}} + 2\right) e^{x^{e^{1}}}}{x^{3}}
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