Derivada de (lnx)^sqrt(x)

Ha introducido [src]

          ___
        \/ x 
(log(x))

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

log(x)^(sqrt(x))

Solución detallada

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Perola derivada

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

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

              /                      2      4                 \
              |/  2                 \    ------- + log(log(x))|
          ___ ||------ + log(log(x))|       2                 |
        \/ x  |\log(x)              /    log (x)              |
(log(x))     *|----------------------- - ---------------------|
              |           x                        3/2        |
              \                                   x           /
---------------------------------------------------------------
                               4

$$\frac{\left(\frac{\left(\log{\left(\log{\left(x \right)} \right)} + \frac{2}{\log{\left(x \right)}}\right)^{2}}{x} - \frac{\log{\left(\log{\left(x \right)} \right)} + \frac{4}{\log{\left(x \right)}^{2}}}{x^{\frac{3}{2}}}\right) \log{\left(x \right)}^{\sqrt{x}}}{4}$$

Simplificar

Tercera derivada [src]

              /    2                         12        16                           3     /  2                 \ /   4                 \\
              |- ------ + 3*log(log(x)) + ------- + -------   /  2                 \    3*|------ + log(log(x))|*|------- + log(log(x))||
          ___ |  log(x)                      2         3      |------ + log(log(x))|      \log(x)              / |   2                 ||
        \/ x  |                           log (x)   log (x)   \log(x)              /                             \log (x)              /|
(log(x))     *|-------------------------------------------- + ----------------------- - ------------------------------------------------|
              |                     5/2                                  3/2                                    2                       |
              \                    x                                    x                                      x                        /
-----------------------------------------------------------------------------------------------------------------------------------------
                                                                    8

$$\frac{\left(- \frac{3 \left(\log{\left(\log{\left(x \right)} \right)} + \frac{4}{\log{\left(x \right)}^{2}}\right) \left(\log{\left(\log{\left(x \right)} \right)} + \frac{2}{\log{\left(x \right)}}\right)}{x^{2}} + \frac{\left(\log{\left(\log{\left(x \right)} \right)} + \frac{2}{\log{\left(x \right)}}\right)^{3}}{x^{\frac{3}{2}}} + \frac{3 \log{\left(\log{\left(x \right)} \right)} - \frac{2}{\log{\left(x \right)}} + \frac{12}{\log{\left(x \right)}^{2}} + \frac{16}{\log{\left(x \right)}^{3}}}{x^{\frac{5}{2}}}\right) \log{\left(x \right)}^{\sqrt{x}}}{8}$$

Simplificar

Gráfico

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Derivada de (lnx)^sqrt(x)

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