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x^(log(x)/log(10))
Derivada de la función/ log(x)/ (log(x)/log(10))/ x^(log(x)/log(10))

Derivada de x^(log(x)/log(10))

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

Gráfico:

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Solución

Ha introducido [src] 
  log(x)
 -------
 log(10)
x
xlog⁡(x)log⁡(10)x^{\frac{\log{\left(x \right)}}{\log{\left(10 \right)}}} 
x^(log(x)/log(10))
Solución detallada

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

    Perola derivada

    (log⁡(x)log⁡(10))log⁡(x)log⁡(10)(log⁡(log⁡(x)log⁡(10))+1)\left(\frac{\log{\left(x \right)}}{\log{\left(10 \right)}}\right)^{\frac{\log{\left(x \right)}}{\log{\left(10 \right)}}} \left(\log{\left(\frac{\log{\left(x \right)}}{\log{\left(10 \right)}} \right)} + 1\right)

  2. Simplificamos:

    (log⁡(x)log⁡(10))log⁡(x)log⁡(10)(log⁡(log⁡(x)log⁡(10))+1)\left(\frac{\log{\left(x \right)}}{\log{\left(10 \right)}}\right)^{\frac{\log{\left(x \right)}}{\log{\left(10 \right)}}} \left(\log{\left(\frac{\log{\left(x \right)}}{\log{\left(10 \right)}} \right)} + 1\right)

Respuesta:

(log⁡(x)log⁡(10))log⁡(x)log⁡(10)(log⁡(log⁡(x)log⁡(10))+1)\left(\frac{\log{\left(x \right)}}{\log{\left(10 \right)}}\right)^{\frac{\log{\left(x \right)}}{\log{\left(10 \right)}}} \left(\log{\left(\frac{\log{\left(x \right)}}{\log{\left(10 \right)}} \right)} + 1\right)

Gráfica
02468-8-6-4-2-1010-200200
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    log(x)       
   -------       
   log(10)       
2*x       *log(x)
-----------------
    x*log(10)
2xlog⁡(x)log⁡(10)log⁡(x)xlog⁡(10)\frac{2 x^{\frac{\log{\left(x \right)}}{\log{\left(10 \right)}}} \log{\left(x \right)}}{x \log{\left(10 \right)}}
Simplificar
Segunda derivada [src] 
    log(x)                         
   ------- /                  2   \
   log(10) |             2*log (x)|
2*x       *|1 - log(x) + ---------|
           \              log(10) /
-----------------------------------
              2                    
             x *log(10)
2xlog⁡(x)log⁡(10)(2log⁡(x)2log⁡(10)−log⁡(x)+1)x2log⁡(10)\frac{2 x^{\frac{\log{\left(x \right)}}{\log{\left(10 \right)}}} \left(\frac{2 \log{\left(x \right)}^{2}}{\log{\left(10 \right)}} - \log{\left(x \right)} + 1\right)}{x^{2} \log{\left(10 \right)}}
Simplificar
Tercera derivada [src] 
    log(x)                                                   
   ------- /                     2           3              \
   log(10) |                6*log (x)   4*log (x)   6*log(x)|
2*x       *|-3 + 2*log(x) - --------- + --------- + --------|
           |                 log(10)        2       log(10) |
           \                             log (10)           /
-------------------------------------------------------------
                           3                                 
                          x *log(10)
2xlog⁡(x)log⁡(10)(4log⁡(x)3log⁡(10)2−6log⁡(x)2log⁡(10)+2log⁡(x)+6log⁡(x)log⁡(10)−3)x3log⁡(10)\frac{2 x^{\frac{\log{\left(x \right)}}{\log{\left(10 \right)}}} \left(\frac{4 \log{\left(x \right)}^{3}}{\log{\left(10 \right)}^{2}} - \frac{6 \log{\left(x \right)}^{2}}{\log{\left(10 \right)}} + 2 \log{\left(x \right)} + \frac{6 \log{\left(x \right)}}{\log{\left(10 \right)}} - 3\right)}{x^{3} \log{\left(10 \right)}}
Simplificar
Gráfico
Derivada de x^(log(x)/log(10))
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