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x^log4(x)
Derivada de la función/ x^log4(x)

Derivada de x^log4(x)

Función f() - derivada -er orden en el punto
v

Gráfico:

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Solución

Ha introducido [src] 
 log(x)
 ------
 log(4)
x
xlog⁡(x)log⁡(4)x^{\frac{\log{\left(x \right)}}{\log{\left(4 \right)}}} 
x^(log(x)/log(4))
Solución detallada

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

    Perola derivada

    (log⁡(x)log⁡(4))log⁡(x)log⁡(4)(log⁡(log⁡(x)log⁡(4))+1)\left(\frac{\log{\left(x \right)}}{\log{\left(4 \right)}}\right)^{\frac{\log{\left(x \right)}}{\log{\left(4 \right)}}} \left(\log{\left(\frac{\log{\left(x \right)}}{\log{\left(4 \right)}} \right)} + 1\right)

  2. Simplificamos:

    (log⁡(x)log⁡(4))log⁡(x)log⁡(4)(log⁡(log⁡(x)log⁡(4))+1)\left(\frac{\log{\left(x \right)}}{\log{\left(4 \right)}}\right)^{\frac{\log{\left(x \right)}}{\log{\left(4 \right)}}} \left(\log{\left(\frac{\log{\left(x \right)}}{\log{\left(4 \right)}} \right)} + 1\right)

Respuesta:

(log⁡(x)log⁡(4))log⁡(x)log⁡(4)(log⁡(log⁡(x)log⁡(4))+1)\left(\frac{\log{\left(x \right)}}{\log{\left(4 \right)}}\right)^{\frac{\log{\left(x \right)}}{\log{\left(4 \right)}}} \left(\log{\left(\frac{\log{\left(x \right)}}{\log{\left(4 \right)}} \right)} + 1\right)

Gráfica
02468-8-6-4-2-1010-20002000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   log(x)       
   ------       
   log(4)       
2*x      *log(x)
----------------
    x*log(4)
2xlog⁡(x)log⁡(4)log⁡(x)xlog⁡(4)\frac{2 x^{\frac{\log{\left(x \right)}}{\log{\left(4 \right)}}} \log{\left(x \right)}}{x \log{\left(4 \right)}}
Simplificar
Segunda derivada [src] 
   log(x)                         
   ------ /                  2   \
   log(4) |             2*log (x)|
2*x      *|1 - log(x) + ---------|
          \               log(4) /
----------------------------------
             2                    
            x *log(4)
2xlog⁡(x)log⁡(4)(2log⁡(x)2log⁡(4)−log⁡(x)+1)x2log⁡(4)\frac{2 x^{\frac{\log{\left(x \right)}}{\log{\left(4 \right)}}} \left(\frac{2 \log{\left(x \right)}^{2}}{\log{\left(4 \right)}} - \log{\left(x \right)} + 1\right)}{x^{2} \log{\left(4 \right)}}
Simplificar
Tercera derivada [src] 
   log(x)                                                   
   ------ /                     2           3              \
   log(4) |                6*log (x)   4*log (x)   6*log(x)|
2*x      *|-3 + 2*log(x) - --------- + --------- + --------|
          |                  log(4)        2        log(4) |
          \                             log (4)            /
------------------------------------------------------------
                          3                                 
                         x *log(4)
2xlog⁡(x)log⁡(4)(4log⁡(x)3log⁡(4)2−6log⁡(x)2log⁡(4)+2log⁡(x)+6log⁡(x)log⁡(4)−3)x3log⁡(4)\frac{2 x^{\frac{\log{\left(x \right)}}{\log{\left(4 \right)}}} \left(\frac{4 \log{\left(x \right)}^{3}}{\log{\left(4 \right)}^{2}} - \frac{6 \log{\left(x \right)}^{2}}{\log{\left(4 \right)}} + 2 \log{\left(x \right)} + \frac{6 \log{\left(x \right)}}{\log{\left(4 \right)}} - 3\right)}{x^{3} \log{\left(4 \right)}}
Simplificar
Gráfico
Derivada de x^log4(x)
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