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

Derivada de x^(loge(x))

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

Gráfico:

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Solución

Ha introducido [src] 
  log(x)
 -------
    / 1\
 log\e /
x
xlog⁡(x)log⁡(e1)x^{\frac{\log{\left(x \right)}}{\log{\left(e^{1} \right)}}} 
x^(log(x)/log(exp(1)))
Solución detallada

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

    Perola derivada

    (log⁡(x)log⁡(e1))log⁡(x)log⁡(e1)(log⁡(log⁡(x)log⁡(e1))+1)\left(\frac{\log{\left(x \right)}}{\log{\left(e^{1} \right)}}\right)^{\frac{\log{\left(x \right)}}{\log{\left(e^{1} \right)}}} \left(\log{\left(\frac{\log{\left(x \right)}}{\log{\left(e^{1} \right)}} \right)} + 1\right)

  2. Simplificamos:

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-1000010000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    log(x)       
   -------       
      / 1\       
   log\e /       
2*x       *log(x)
-----------------
         / 1\    
    x*log\e /
2xlog⁡(x)log⁡(e1)log⁡(x)xlog⁡(e1)\frac{2 x^{\frac{\log{\left(x \right)}}{\log{\left(e^{1} \right)}}} \log{\left(x \right)}}{x \log{\left(e^{1} \right)}}
Simplificar
Segunda derivada [src] 
    log(x)                         
   -------                         
      / 1\ /                  2   \
   log\e / |             2*log (x)|
2*x       *|1 - log(x) + ---------|
           |                 / 1\ |
           \              log\e / /
-----------------------------------
              2    / 1\            
             x *log\e /
2xlog⁡(x)log⁡(e1)(2log⁡(x)2log⁡(e1)−log⁡(x)+1)x2log⁡(e1)\frac{2 x^{\frac{\log{\left(x \right)}}{\log{\left(e^{1} \right)}}} \left(\frac{2 \log{\left(x \right)}^{2}}{\log{\left(e^{1} \right)}} - \log{\left(x \right)} + 1\right)}{x^{2} \log{\left(e^{1} \right)}}
Simplificar
Tercera derivada [src] 
    log(x)                                                   
   -------                                                   
      / 1\ /                     2           3              \
   log\e / |                6*log (x)   4*log (x)   6*log(x)|
2*x       *|-3 + 2*log(x) - --------- + --------- + --------|
           |                    / 1\        2/ 1\      / 1\ |
           \                 log\e /     log \e /   log\e / /
-------------------------------------------------------------
                           3    / 1\                         
                          x *log\e /
2xlog⁡(x)log⁡(e1)(4log⁡(x)3log⁡(e1)2−6log⁡(x)2log⁡(e1)+2log⁡(x)+6log⁡(x)log⁡(e1)−3)x3log⁡(e1)\frac{2 x^{\frac{\log{\left(x \right)}}{\log{\left(e^{1} \right)}}} \left(\frac{4 \log{\left(x \right)}^{3}}{\log{\left(e^{1} \right)}^{2}} - \frac{6 \log{\left(x \right)}^{2}}{\log{\left(e^{1} \right)}} + 2 \log{\left(x \right)} + \frac{6 \log{\left(x \right)}}{\log{\left(e^{1} \right)}} - 3\right)}{x^{3} \log{\left(e^{1} \right)}}
Simplificar
Gráfico
Derivada de x^(loge(x))
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