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Derivada de la función/ (x)^x/ (x^x)/ (x)^(x)/ x+(x^x)+((x)^(x)^x)

Derivada de x+(x^x)+((x)^(x)^x)

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

Ha introducido [src] 
          / x\
     x    \x /
x + x  + x
xxx+(x+xx)x^{x^{x}} + \left(x + x^{x}\right) 
x + x^x + x^(x^x)
Solución detallada

  1. diferenciamos xxx+(x+xx)x^{x^{x}} + \left(x + x^{x}\right) miembro por miembro:

    1. diferenciamos x+xxx + x^{x} miembro por miembro:

      1. Según el principio, aplicamos: xx tenemos 11

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

        Perola derivada

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

      Como resultado de: xx(log⁡(x)+1)+1x^{x} \left(\log{\left(x \right)} + 1\right) + 1

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

      Perola derivada

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

    Como resultado de: xx(log⁡(x)+1)+(log⁡(xx)+1)(xx)xx+1x^{x} \left(\log{\left(x \right)} + 1\right) + \left(\log{\left(x^{x} \right)} + 1\right) \left(x^{x}\right)^{x^{x}} + 1

Respuesta:

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

Primera derivada [src] 
                       / x\ / x                         \
     x                 \x / |x     x                    |
1 + x *(1 + log(x)) + x    *|-- + x *(1 + log(x))*log(x)|
                            \x                          /
xx(log⁡(x)+1)+xxx(xx(log⁡(x)+1)log⁡(x)+xxx)+1x^{x} \left(\log{\left(x \right)} + 1\right) + x^{x^{x}} \left(x^{x} \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{x^{x}}{x}\right) + 1
Simplificar
Segunda derivada [src] 
   /                     / x\                                                               / x\                          2\
 x |1               2    \x / /  1    log(x)               2          2*(1 + log(x))\    x  \x / /1                      \ |
x *|- + (1 + log(x))  + x    *|- -- + ------ + (1 + log(x)) *log(x) + --------------| + x *x    *|- + (1 + log(x))*log(x)| |
   |x                         |   2     x                                   x       |            \x                      / |
   \                          \  x                                                  /                                      /
xx(xxxxx((log⁡(x)+1)log⁡(x)+1x)2+xxx((log⁡(x)+1)2log⁡(x)+2(log⁡(x)+1)x+log⁡(x)x−1x2)+(log⁡(x)+1)2+1x)x^{x} \left(x^{x} x^{x^{x}} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} + x^{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) + \left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right)
Simplificar
Tercera derivada [src] 
   /                      / x\ /                                                                         2                        \                     / x\                               3         / x\                                                                                  \
 x |            3   1     \x / |2    3                3          log(x)   3*(1 + log(x))   3*(1 + log(x))    3*(1 + log(x))*log(x)|   3*(1 + log(x))    \x /  2*x /1                      \       x  \x / /1                      \ /  1    log(x)               2          2*(1 + log(x))\|
x *|(1 + log(x))  - -- + x    *|-- + -- + (1 + log(x)) *log(x) - ------ - -------------- + --------------- + ---------------------| + -------------- + x    *x   *|- + (1 + log(x))*log(x)|  + 3*x *x    *|- + (1 + log(x))*log(x)|*|- -- + ------ + (1 + log(x)) *log(x) + --------------||
   |                 2         | 3    2                             2            2                x                    x          |         x                     \x                      /               \x                      / |   2     x                                   x       ||
   \                x          \x    x                             x            x                                                 /                                                                                                 \  x                                                  //
xx(x2xxxx((log⁡(x)+1)log⁡(x)+1x)3+3xxxxx((log⁡(x)+1)log⁡(x)+1x)((log⁡(x)+1)2log⁡(x)+2(log⁡(x)+1)x+log⁡(x)x−1x2)+xxx((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)+1)3+3(log⁡(x)+1)x−1x2)x^{x} \left(x^{2 x} x^{x^{x}} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 x^{x} x^{x^{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) + x^{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) + \left(\log{\left(x \right)} + 1\right)^{3} + \frac{3 \left(\log{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right)
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