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x^(ln(16x))
Derivada de la función/ x^(ln(16x))

Derivada de x^(ln(16x))

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
 log(16*x)
x
xlog⁡(16x)x^{\log{\left(16 x \right)}} 
x^log(16*x)
Solución detallada

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

    Perola derivada

    (log⁡(log⁡(16x))+1)log⁡(16x)log⁡(16x)\left(\log{\left(\log{\left(16 x \right)} \right)} + 1\right) \log{\left(16 x \right)}^{\log{\left(16 x \right)}}

Respuesta:

(log⁡(log⁡(16x))+1)log⁡(16x)log⁡(16x)\left(\log{\left(\log{\left(16 x \right)} \right)} + 1\right) \log{\left(16 x \right)}^{\log{\left(16 x \right)}}

Gráfica
02468-8-6-4-2-1010200000-100000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 log(16*x) /log(x)   log(16*x)\
x         *|------ + ---------|
           \  x          x    /
xlog⁡(16x)(log⁡(x)x+log⁡(16x)x)x^{\log{\left(16 x \right)}} \left(\frac{\log{\left(x \right)}}{x} + \frac{\log{\left(16 x \right)}}{x}\right)
Simplificar
Segunda derivada [src] 
 log(16*x) /                        2                     \
x         *\2 + (log(x) + log(16*x))  - log(x) - log(16*x)/
-----------------------------------------------------------
                              2                            
                             x
xlog⁡(16x)((log⁡(x)+log⁡(16x))2−log⁡(x)−log⁡(16x)+2)x2\frac{x^{\log{\left(16 x \right)}} \left(\left(\log{\left(x \right)} + \log{\left(16 x \right)}\right)^{2} - \log{\left(x \right)} - \log{\left(16 x \right)} + 2\right)}{x^{2}}
Simplificar
Tercera derivada [src] 
 log(16*x) /                         3                                                                            \
x         *\-6 + (log(x) + log(16*x))  + 2*log(x) + 2*log(16*x) - 3*(log(x) + log(16*x))*(-2 + log(x) + log(16*x))/
-------------------------------------------------------------------------------------------------------------------
                                                          3                                                        
                                                         x
xlog⁡(16x)((log⁡(x)+log⁡(16x))3−3(log⁡(x)+log⁡(16x))(log⁡(x)+log⁡(16x)−2)+2log⁡(x)+2log⁡(16x)−6)x3\frac{x^{\log{\left(16 x \right)}} \left(\left(\log{\left(x \right)} + \log{\left(16 x \right)}\right)^{3} - 3 \left(\log{\left(x \right)} + \log{\left(16 x \right)}\right) \left(\log{\left(x \right)} + \log{\left(16 x \right)} - 2\right) + 2 \log{\left(x \right)} + 2 \log{\left(16 x \right)} - 6\right)}{x^{3}}
Simplificar
Gráfico
Derivada de x^(ln(16x))
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