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Derivada de la función/ ln(x)/ (x)^x/ x^(x^3+ln(x)^x)

Derivada de x^(x^3+ln(x)^x)

Solución

Ha introducido [src]

  3      x   
 x  + log (x)
x

x^{x^{3} + \log{\left(x \right)}^{x}}

x^(x^3 + log(x)^x)

Solución detallada

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

Perola derivada

$\left(x^{3} + \log{\left(x \right)}^{x}\right)^{x^{3} + \log{\left(x \right)}^{x}} \left(\log{\left(x^{3} + \log{\left(x \right)}^{x} \right)} + 1\right)$

Respuesta:

$\left(x^{3} + \log{\left(x \right)}^{x}\right)^{x^{3} + \log{\left(x \right)}^{x}} \left(\log{\left(x^{3} + \log{\left(x \right)}^{x} \right)} + 1\right)$

Primera derivada [src]

  3      x    / 3      x                                                    \
 x  + log (x) |x  + log (x)   /   2      x    /  1                 \\       |
x            *|------------ + |3*x  + log (x)*|------ + log(log(x))||*log(x)|
              \     x         \               \log(x)              //       /

x^{x^{3} + \log{\left(x \right)}^{x}} \left(\left(3 x^{2} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}\right) \log{\left(x \right)} + \frac{x^{3} + \log{\left(x \right)}^{x}}{x}\right)

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Segunda derivada [src]

              /                                                               2   /                                           x    /      1   \\                           /   2      x    /  1                 \\\
  3      x    |/ 3      x                                                    \    |                            2           log (x)*|1 - ------||           3      x      2*|3*x  + log (x)*|------ + log(log(x))|||
 x  + log (x) ||x  + log (x)   /   2      x    /  1                 \\       |    |      /  1                 \     x              \    log(x)/|          x  + log (x)     \               \log(x)              //|
x            *||------------ + |3*x  + log (x)*|------ + log(log(x))||*log(x)|  + |6*x + |------ + log(log(x))| *log (x) + --------------------|*log(x) - ------------ + -----------------------------------------|
              |\     x         \               \log(x)              //       /    \      \log(x)              /                  x*log(x)      /                2                            x                    |
              \                                                                                                                                                x                                                  /

x^{x^{3} + \log{\left(x \right)}^{x}} \left(\left(\left(3 x^{2} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}\right) \log{\left(x \right)} + \frac{x^{3} + \log{\left(x \right)}^{x}}{x}\right)^{2} + \left(6 x + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} \log{\left(x \right)}^{x} + \frac{\left(1 - \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}}{x \log{\left(x \right)}}\right) \log{\left(x \right)} + \frac{2 \left(3 x^{2} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}\right)}{x} - \frac{x^{3} + \log{\left(x \right)}^{x}}{x^{2}}\right)

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Tercera derivada [src]

              /                                                                                                                                                                                                                                                           /                                           x    /      1   \\                                                                                                                                                                                                       \
              |                                                                   /                                         x    /       2   \                                                \                                                                           |                            2           log (x)*|1 - ------||                                                                                                                                                                                                       |
              |                                                               3   |                                      log (x)*|1 - -------|        x    /      1   \ /  1                 \|            /   2      x    /  1                 \\                        |      /  1                 \     x              \    log(x)/|                                                                     //                                           x    /      1   \\                           /   2      x    /  1                 \\\|
  3      x    |/ 3      x                                                    \    |                          3                   |       2   |   3*log (x)*|1 - ------|*|------ + log(log(x))||          3*|3*x  + log (x)*|------ + log(log(x))||     / 3      x   \   3*|6*x + |------ + log(log(x))| *log (x) + --------------------|     / 3      x                                                    \ ||                            2           log (x)*|1 - ------||           3      x      2*|3*x  + log (x)*|------ + log(log(x))||||
 x  + log (x) ||x  + log (x)   /   2      x    /  1                 \\       |    |    /  1                 \     x              \    log (x)/             \    log(x)/ \log(x)              /|            \               \log(x)              //   2*\x  + log (x)/     \      \log(x)              /                  x*log(x)      /     |x  + log (x)   /   2      x    /  1                 \\       | ||      /  1                 \     x              \    log(x)/|          x  + log (x)     \               \log(x)              //||
x            *||------------ + |3*x  + log (x)*|------ + log(log(x))||*log(x)|  + |6 + |------ + log(log(x))| *log (x) - --------------------- + ---------------------------------------------|*log(x) - ----------------------------------------- + ---------------- + ---------------------------------------------------------------- + 3*|------------ + |3*x  + log (x)*|------ + log(log(x))||*log(x)|*||6*x + |------ + log(log(x))| *log (x) + --------------------|*log(x) - ------------ + -----------------------------------------||
              |\     x         \               \log(x)              //       /    |    \log(x)              /                   2                                   x*log(x)                  |                               2                              3                                         x                                     \     x         \               \log(x)              //       / |\      \log(x)              /                  x*log(x)      /                2                            x                    ||
              \                                                                   \                                            x *log(x)                                                      /                              x                              x                                                                                                                                                \                                                                             x                                                  //

x^{x^{3} + \log{\left(x \right)}^{x}} \left(\left(\left(3 x^{2} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}\right) \log{\left(x \right)} + \frac{x^{3} + \log{\left(x \right)}^{x}}{x}\right)^{3} + 3 \left(\left(3 x^{2} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}\right) \log{\left(x \right)} + \frac{x^{3} + \log{\left(x \right)}^{x}}{x}\right) \left(\left(6 x + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} \log{\left(x \right)}^{x} + \frac{\left(1 - \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}}{x \log{\left(x \right)}}\right) \log{\left(x \right)} + \frac{2 \left(3 x^{2} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}\right)}{x} - \frac{x^{3} + \log{\left(x \right)}^{x}}{x^{2}}\right) + \left(\left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{3} \log{\left(x \right)}^{x} + 6 + \frac{3 \left(1 - \frac{1}{\log{\left(x \right)}}\right) \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}}{x \log{\left(x \right)}} - \frac{\left(1 - \frac{2}{\log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{x}}{x^{2} \log{\left(x \right)}}\right) \log{\left(x \right)} + \frac{3 \left(6 x + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} \log{\left(x \right)}^{x} + \frac{\left(1 - \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}}{x \log{\left(x \right)}}\right)}{x} - \frac{3 \left(3 x^{2} + \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}\right)}{x^{2}} + \frac{2 \left(x^{3} + \log{\left(x \right)}^{x}\right)}{x^{3}}\right)

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Derivada de x^(x^3+ln(x)^x)

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