Derivada de xln(x)^x^2

Solución

Ha introducido [src]

          / 2\
          \x /
x*(log(x))

$$x \log{\left(x \right)}^{x^{2}}$$

x*log(x)^(x^2)

Solución detallada

Se aplica la regla de la derivada de una multiplicación:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = x$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
1. Según el principio, aplicamos: $x$ tenemos $1$
$g{\left(x \right)} = \log{\left(x \right)}^{x^{2}}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
1. No logro encontrar los pasos en la búsqueda de esta derivada.
  
  Perola derivada
  
  $\left(\log{\left(x^{2} \right)} + 1\right) \left|{x}\right|^{2 x^{2}}$
Como resultado de: $x \left(\log{\left(x^{2} \right)} + 1\right) \left|{x}\right|^{2 x^{2}} + \log{\left(x \right)}^{x^{2}}$

Respuesta:

$x \left(\log{\left(x^{2} \right)} + 1\right) \left|{x}\right|^{2 x^{2}} + \log{\left(x \right)}^{x^{2}}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

          / 2\ /                                                                2\
          \x / |     1        5                       2 /  1                   \ |
x*(log(x))    *|- ------- + ------ + 6*log(log(x)) + x *|------ + 2*log(log(x))| |
               |     2      log(x)                      \log(x)                / |
               \  log (x)                                                        /

$$x \left(x^{2} \left(2 \log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} + 6 \log{\left(\log{\left(x \right)} \right)} + \frac{5}{\log{\left(x \right)}} - \frac{1}{\log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{x^{2}}$$

Simplificar

Tercera derivada [src]

             /                                       /                                     3         2                                                                       \                                 \
             |                                       |                               2 - ------ + -------                                                                    |                                 |
        / 2\ |                                       |                           3       log(x)      2                                                                       |                                2|
        \x / |     3                        9        | 3 /  1                   \                 log (x)       /  1                   \ /     1                        3   \|      2 /  1                   \ |
(log(x))    *|- ------- + 6*log(log(x)) + ------ + x*|x *|------ + 2*log(log(x))|  + -------------------- + 3*x*|------ + 2*log(log(x))|*|- ------- + 2*log(log(x)) + ------|| + 3*x *|------ + 2*log(log(x))| |
             |     2                      log(x)     |   \log(x)                /          x*log(x)             \log(x)                / |     2                      log(x)||        \log(x)                / |
             \  log (x)                              \                                                                                   \  log (x)                         //                                 /

$$\left(3 x^{2} \left(2 \log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} + x \left(x^{3} \left(2 \log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{3} + 3 x \left(2 \log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \left(2 \log{\left(\log{\left(x \right)} \right)} + \frac{3}{\log{\left(x \right)}} - \frac{1}{\log{\left(x \right)}^{2}}\right) + \frac{2 - \frac{3}{\log{\left(x \right)}} + \frac{2}{\log{\left(x \right)}^{2}}}{x \log{\left(x \right)}}\right) + 6 \log{\left(\log{\left(x \right)} \right)} + \frac{9}{\log{\left(x \right)}} - \frac{3}{\log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{x^{2}}$$

Simplificar

Gráfico

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Derivada de xln(x)^x^2

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