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Derivada de la función/ x^x^x/ x^x^x^x^x

Derivada de x^x^x^x^x

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
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 | \x    /|
 \x       /
x
xxxxxx^{x^{x^{x^{x}}}} 
x^(x^(x^(x^x)))
Solución detallada

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

    Perola derivada

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

Respuesta:

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

Primera derivada [src] 
 / / / x\\\ / / / x\\                                                                       \
 | | \x /|| | | \x /|    / / x\\ / / x\                                             \       |
 | \x    /| | \x    /    | \x /| | \x /    / x\ / x                         \       |       |
 \x       / |x           \x    / |x        \x / |x     x                    |       |       |
x          *|-------- + x       *|----- + x    *|-- + x *(1 + log(x))*log(x)|*log(x)|*log(x)|
            \   x                \  x           \x                          /       /       /
xxxxx(xxxx(xxx(xx(log⁡(x)+1)log⁡(x)+xxx)log⁡(x)+xxxx)log⁡(x)+xxxxx)x^{x^{x^{x^{x}}}} \left(x^{x^{x^{x}}} \left(x^{x^{x}} \left(x^{x} \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{x^{x}}{x}\right) \log{\left(x \right)} + \frac{x^{x^{x}}}{x}\right) \log{\left(x \right)} + \frac{x^{x^{x^{x}}}}{x}\right)
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Segunda derivada [src] 
          / / / x\\\ /                                                                                                                                                                                                                                                                                                                 / x\                                          \
 / / x\\  | | \x /|| |        / / x\\                                                             2         /                                                                                                                       x /1                      \\                                                                       \x / /1    x /1                      \       \|
 | \x /|  | \x    /| |        | \x /| /     / x\                                                 \     / x\ |                                                                                                         2          2*x *|- + (1 + log(x))*log(x)||              x                                          2          2*x    *|- + x *|- + (1 + log(x))*log(x)|*log(x)||
 \x    /  \x       / |  1     \x    / |1    \x / /1    x /1                      \       \       |     \x / |  1     x /  1    log(x)               2          2*(1 + log(x))\           2*x /1                      \                \x                      /|           2*x  /1    x /1                      \       \                   \x      \x                      /       /|
x       *x          *|- -- + x       *|- + x    *|- + x *|- + (1 + log(x))*log(x)|*log(x)|*log(x)|  + x    *|- -- + x *|- -- + ------ + (1 + log(x)) *log(x) + --------------|*log(x) + x   *|- + (1 + log(x))*log(x)| *log(x) + ------------------------------|*log(x) + x    *|- + x *|- + (1 + log(x))*log(x)|*log(x)| *log(x) + -------------------------------------------------|
                     |   2            \x         \x      \x                      /       /       /          |   2      |   2     x                                   x       |               \x                      /                         x               |                \x      \x                      /       /                                   x                        |
                     \  x                                                                                   \  x       \  x                                                  /                                                                                 /                                                                                                                     /
xxxxxxxxx(x2xx(xx((log⁡(x)+1)log⁡(x)+1x)log⁡(x)+1x)2log⁡(x)+xxx(x2x((log⁡(x)+1)log⁡(x)+1x)2log⁡(x)+xx((log⁡(x)+1)2log⁡(x)+2(log⁡(x)+1)x+log⁡(x)x−1x2)log⁡(x)+2xx((log⁡(x)+1)log⁡(x)+1x)x−1x2)log⁡(x)+xxxx(xxx(xx((log⁡(x)+1)log⁡(x)+1x)log⁡(x)+1x)log⁡(x)+1x)2+2xxx(xx((log⁡(x)+1)log⁡(x)+1x)log⁡(x)+1x)x−1x2)x^{x^{x^{x}}} x^{x^{x^{x^{x}}}} \left(x^{2 x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} \log{\left(x \right)} + x^{x^{x}} \left(x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} \log{\left(x \right)} + x^{x} \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + \frac{2 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + x^{x^{x^{x}}} \left(x^{x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \frac{2 x^{x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x} - \frac{1}{x^{2}}\right)
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Tercera derivada [src] 
                     /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        /                                                                                                                       x /1                      \\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        \
                     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   / x\ |                                                                                                         2          2*x *|- + (1 + log(x))*log(x)||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        |
          / / / x\\\ |                                                                                    /                                                                                                                                                                                                   x /  1    log(x)               2          2*(1 + log(x))\                                   2                                                                                                  \                                                                       / x\                                                \x / |  1     x /  1    log(x)               2          2*(1 + log(x))\           2*x /1                      \                \x                      /|         x                                          2                                                                           /                                                                                                                                                                                                                                        / x\                                          \                                                                                                                                                                                                                |
 / / x\\  | | \x /|| |         / x\                                                             3         |                                                                                                                                                                  x /1                      \   3*x *|- -- + ------ + (1 + log(x)) *log(x) + --------------|      2*x /1                      \                                                                                                   |                                                                       \x / /1    x /1                      \       \   3*x    *|- -- + x *|- -- + ------ + (1 + log(x)) *log(x) + --------------|*log(x) + x   *|- + (1 + log(x))*log(x)| *log(x) + ------------------------------|      2*x  /1    x /1                      \       \       / / x\\                                                              |             /                                                                                                                       x /1                      \\                                                                       \x / /1    x /1                      \       \|                                                     /                                                                                                                       x /1                      \\       |
 | \x /|  | \x    /| |         \x / /     / x\                                                 \     / x\ |        /                                                                         2                        \                                        3          3*x *|- + (1 + log(x))*log(x)|        |   2     x                                   x       |   3*x   *|- + (1 + log(x))*log(x)|                                                                                                   |              x                                          3          3*x    *|- + x *|- + (1 + log(x))*log(x)|*log(x)|           |   2      |   2     x                                   x       |               \x                      /                         x               |   3*x    *|- + x *|- + (1 + log(x))*log(x)|*log(x)|       | \x /| /     / x\                                                 \ |        / x\ |                                                                                                         2          2*x *|- + (1 + log(x))*log(x)||              x                                          2          2*x    *|- + x *|- + (1 + log(x))*log(x)|*log(x)||         x                                           |                                                                                                         2          2*x *|- + (1 + log(x))*log(x)||       |
 \x    /  \x       / |2     2*x     |1    \x / /1    x /1                      \       \       |     \x / |2     x |2    3                3          log(x)   3*(1 + log(x))   3*(1 + log(x))    3*(1 + log(x))*log(x)|           3*x /1                      \                \x                      /        \  x                                                  /          \x                      /       2*x /1                      \ /  1    log(x)               2          2*(1 + log(x))\       |           3*x  /1    x /1                      \       \                   \x      \x                      /       /           \  x       \  x                                                  /                                                                                 /           \x      \x                      /       /       \x    / |1    \x / /1    x /1                      \       \       | |  1     \x / |  1     x /  1    log(x)               2          2*(1 + log(x))\           2*x /1                      \                \x                      /|           2*x  /1    x /1                      \       \                   \x      \x                      /       /|      2*x  /1    x /1                      \       \ |  1     x /  1    log(x)               2          2*(1 + log(x))\           2*x /1                      \                \x                      /|       |
x       *x          *|-- + x       *|- + x    *|- + x *|- + (1 + log(x))*log(x)|*log(x)|*log(x)|  + x    *|-- + x *|-- + -- + (1 + log(x)) *log(x) - ------ - -------------- + --------------- + ---------------------|*log(x) + x   *|- + (1 + log(x))*log(x)| *log(x) - ------------------------------ + ------------------------------------------------------------ + --------------------------------- + 3*x   *|- + (1 + log(x))*log(x)|*|- -- + ------ + (1 + log(x)) *log(x) + --------------|*log(x)|*log(x) + x    *|- + x *|- + (1 + log(x))*log(x)|*log(x)| *log(x) - ------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------- + 3*x       *|- + x    *|- + x *|- + (1 + log(x))*log(x)|*log(x)|*log(x)|*|- -- + x    *|- -- + x *|- -- + ------ + (1 + log(x)) *log(x) + --------------|*log(x) + x   *|- + (1 + log(x))*log(x)| *log(x) + ------------------------------|*log(x) + x    *|- + x *|- + (1 + log(x))*log(x)|*log(x)| *log(x) + -------------------------------------------------| + 3*x    *|- + x *|- + (1 + log(x))*log(x)|*log(x)|*|- -- + x *|- -- + ------ + (1 + log(x)) *log(x) + --------------|*log(x) + x   *|- + (1 + log(x))*log(x)| *log(x) + ------------------------------|*log(x)|
                     | 3            \x         \x      \x                      /       /       /          | 3      | 3    2                             2            2                x                    x          |               \x                      /                          2                                              x                                                 x                          \x                      / |   2     x                                   x       |       |                \x      \x                      /       /                                    2                                                                                                       x                                                                                                         x                                       \x         \x      \x                      /       /       / |   2         |   2      |   2     x                                   x       |               \x                      /                         x               |                \x      \x                      /       /                                   x                        |           \x      \x                      /       / |   2      |   2     x                                   x       |               \x                      /                         x               |       |
                     \x                                                                                   \x       \x    x                             x            x                                                 /                                                                 x                                                                                                                                                      \  x                                                  /       /                                                                                            x                                                                                                                                                                                                                                                                                                                       \  x          \  x       \  x                                                  /                                                                                 /                                                                                                                     /                                                     \  x       \  x                                                  /                                                                                 /       /
xxxxxxxxx(x3xx(xx((log⁡(x)+1)log⁡(x)+1x)log⁡(x)+1x)3log⁡(x)+3x2xx(xx((log⁡(x)+1)log⁡(x)+1x)log⁡(x)+1x)(x2x((log⁡(x)+1)log⁡(x)+1x)2log⁡(x)+xx((log⁡(x)+1)2log⁡(x)+2(log⁡(x)+1)x+log⁡(x)x−1x2)log⁡(x)+2xx((log⁡(x)+1)log⁡(x)+1x)x−1x2)log⁡(x)+xxx(x3x((log⁡(x)+1)log⁡(x)+1x)3log⁡(x)+3x2x((log⁡(x)+1)log⁡(x)+1x)((log⁡(x)+1)2log⁡(x)+2(log⁡(x)+1)x+log⁡(x)x−1x2)log⁡(x)+xx((log⁡(x)+1)3log⁡(x)+3(log⁡(x)+1)2x+3(log⁡(x)+1)log⁡(x)x−3(log⁡(x)+1)x2−log⁡(x)x2+3x2+2x3)log⁡(x)+3x2x((log⁡(x)+1)log⁡(x)+1x)2x+3xx((log⁡(x)+1)2log⁡(x)+2(log⁡(x)+1)x+log⁡(x)x−1x2)x−3xx((log⁡(x)+1)log⁡(x)+1x)x2+2x3)log⁡(x)+x2xxx(xxx(xx((log⁡(x)+1)log⁡(x)+1x)log⁡(x)+1x)log⁡(x)+1x)3+3xxxx(xxx(xx((log⁡(x)+1)log⁡(x)+1x)log⁡(x)+1x)log⁡(x)+1x)(x2xx(xx((log⁡(x)+1)log⁡(x)+1x)log⁡(x)+1x)2log⁡(x)+xxx(x2x((log⁡(x)+1)log⁡(x)+1x)2log⁡(x)+xx((log⁡(x)+1)2log⁡(x)+2(log⁡(x)+1)x+log⁡(x)x−1x2)log⁡(x)+2xx((log⁡(x)+1)log⁡(x)+1x)x−1x2)log⁡(x)+2xxx(xx((log⁡(x)+1)log⁡(x)+1x)log⁡(x)+1x)x−1x2)+3x2xx(xx((log⁡(x)+1)log⁡(x)+1x)log⁡(x)+1x)2x+3xxx(x2x((log⁡(x)+1)log⁡(x)+1x)2log⁡(x)+xx((log⁡(x)+1)2log⁡(x)+2(log⁡(x)+1)x+log⁡(x)x−1x2)log⁡(x)+2xx((log⁡(x)+1)log⁡(x)+1x)x−1x2)x−3xxx(xx((log⁡(x)+1)log⁡(x)+1x)log⁡(x)+1x)x2+2x3)x^{x^{x^{x}}} x^{x^{x^{x^{x}}}} \left(x^{3 x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)^{3} \log{\left(x \right)} + 3 x^{2 x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right) \left(x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} \log{\left(x \right)} + x^{x} \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + \frac{2 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + x^{x^{x}} \left(x^{3 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{3} \log{\left(x \right)} + 3 x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + x^{x} \left(\left(\log{\left(x \right)} + 1\right)^{3} \log{\left(x \right)} + \frac{3 \left(\log{\left(x \right)} + 1\right)^{2}}{x} + \frac{3 \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)}}{x} - \frac{3 \left(\log{\left(x \right)} + 1\right)}{x^{2}} - \frac{\log{\left(x \right)}}{x^{2}} + \frac{3}{x^{2}} + \frac{2}{x^{3}}\right) \log{\left(x \right)} + \frac{3 x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2}}{x} + \frac{3 x^{x} \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right)}{x} - \frac{3 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x^{2}} + \frac{2}{x^{3}}\right) \log{\left(x \right)} + x^{2 x^{x^{x}}} \left(x^{x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 x^{x^{x^{x}}} \left(x^{x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right) \left(x^{2 x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} \log{\left(x \right)} + x^{x^{x}} \left(x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} \log{\left(x \right)} + x^{x} \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + \frac{2 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + \frac{2 x^{x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x} - \frac{1}{x^{2}}\right) + \frac{3 x^{2 x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2}}{x} + \frac{3 x^{x^{x}} \left(x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} \log{\left(x \right)} + x^{x} \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(x \right)} + \frac{2 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x} - \frac{1}{x^{2}}\right)}{x} - \frac{3 x^{x^{x}} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)}{x^{2}} + \frac{2}{x^{3}}\right)
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