Sr Examen

Derivada de x^(loge(x))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src]
  log(x)
 -------
    / 1\
 log\e /
x       
$$x^{\frac{\log{\left(x \right)}}{\log{\left(e^{1} \right)}}}$$
x^(log(x)/log(exp(1)))
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

  2. Simplificamos:


Respuesta:

Gráfica
Primera derivada [src]
    log(x)       
   -------       
      / 1\       
   log\e /       
2*x       *log(x)
-----------------
         / 1\    
    x*log\e /    
$$\frac{2 x^{\frac{\log{\left(x \right)}}{\log{\left(e^{1} \right)}}} \log{\left(x \right)}}{x \log{\left(e^{1} \right)}}$$
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 /            
$$\frac{2 x^{\frac{\log{\left(x \right)}}{\log{\left(e^{1} \right)}}} \left(\frac{2 \log{\left(x \right)}^{2}}{\log{\left(e^{1} \right)}} - \log{\left(x \right)} + 1\right)}{x^{2} \log{\left(e^{1} \right)}}$$
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 /                         
$$\frac{2 x^{\frac{\log{\left(x \right)}}{\log{\left(e^{1} \right)}}} \left(\frac{4 \log{\left(x \right)}^{3}}{\log{\left(e^{1} \right)}^{2}} - \frac{6 \log{\left(x \right)}^{2}}{\log{\left(e^{1} \right)}} + 2 \log{\left(x \right)} + \frac{6 \log{\left(x \right)}}{\log{\left(e^{1} \right)}} - 3\right)}{x^{3} \log{\left(e^{1} \right)}}$$
Gráfico
Derivada de x^(loge(x))