Derivada de x^ln2^x

Ha introducido [src]

    x   
 log (2)
x

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

x^(log(2)^x)

Solución detallada

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Perola derivada

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

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

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

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

Simplificar

Gráfico

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Derivada de x^ln2^x

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