Derivada de x^ln5x

Ha introducido [src]

 log(5*x)
x

x^{\log{\left(5 x \right)}}

x^log(5*x)

Solución detallada

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

Perola derivada

$\left(\log{\left(\log{\left(5 x \right)} \right)} + 1\right) \log{\left(5 x \right)}^{\log{\left(5 x \right)}}$

Respuesta:

$\left(\log{\left(\log{\left(5 x \right)} \right)} + 1\right) \log{\left(5 x \right)}^{\log{\left(5 x \right)}}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

 log(5*x) /log(x)   log(5*x)\
x        *|------ + --------|
          \  x         x    /

x^{\log{\left(5 x \right)}} \left(\frac{\log{\left(x \right)}}{x} + \frac{\log{\left(5 x \right)}}{x}\right)

Simplificar

Segunda derivada [src]

 log(5*x) /                       2                    \
x        *\2 + (log(x) + log(5*x))  - log(x) - log(5*x)/
--------------------------------------------------------
                            2                           
                           x

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

Simplificar

Tercera derivada [src]

 log(5*x) /                        3                                                                         \
x        *\-6 + (log(x) + log(5*x))  + 2*log(x) + 2*log(5*x) - 3*(log(x) + log(5*x))*(-2 + log(x) + log(5*x))/
--------------------------------------------------------------------------------------------------------------
                                                       3                                                      
                                                      x

\frac{x^{\log{\left(5 x \right)}} \left(\left(\log{\left(x \right)} + \log{\left(5 x \right)}\right)^{3} - 3 \left(\log{\left(x \right)} + \log{\left(5 x \right)}\right) \left(\log{\left(x \right)} + \log{\left(5 x \right)} - 2\right) + 2 \log{\left(x \right)} + 2 \log{\left(5 x \right)} - 6\right)}{x^{3}}

Simplificar

Gráfico

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Derivada de x^ln5x

Gráfico:

Definida a trozos:

Solución