Sr Examen

Derivada de x^ln^2x

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

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Definida a trozos:

Solución

Ha introducido [src]
    2   
 log (x)
x       
xlog(x)2x^{\log{\left(x \right)}^{2}}
x^(log(x)^2)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log(log(x)2)+1)(log(x)2)log(x)2\left(\log{\left(\log{\left(x \right)}^{2} \right)} + 1\right) \left(\log{\left(x \right)}^{2}\right)^{\log{\left(x \right)}^{2}}


Respuesta:

(log(log(x)2)+1)(log(x)2)log(x)2\left(\log{\left(\log{\left(x \right)}^{2} \right)} + 1\right) \left(\log{\left(x \right)}^{2}\right)^{\log{\left(x \right)}^{2}}

Gráfica
02468-8-6-4-2-10100500000
Primera derivada [src]
      2           
   log (x)    2   
3*x       *log (x)
------------------
        x         
3xlog(x)2log(x)2x\frac{3 x^{\log{\left(x \right)}^{2}} \log{\left(x \right)}^{2}}{x}
Segunda derivada [src]
      2                                   
   log (x) /                  3   \       
3*x       *\2 - log(x) + 3*log (x)/*log(x)
------------------------------------------
                     2                    
                    x                     
3xlog(x)2(3log(x)3log(x)+2)log(x)x2\frac{3 x^{\log{\left(x \right)}^{2}} \left(3 \log{\left(x \right)}^{3} - \log{\left(x \right)} + 2\right) \log{\left(x \right)}}{x^{2}}
Tercera derivada [src]
      2                                                                   
   log (x) /         4                      2           6            3   \
3*x       *\2 - 9*log (x) - 6*log(x) + 2*log (x) + 9*log (x) + 18*log (x)/
--------------------------------------------------------------------------
                                     3                                    
                                    x                                     
3xlog(x)2(9log(x)69log(x)4+18log(x)3+2log(x)26log(x)+2)x3\frac{3 x^{\log{\left(x \right)}^{2}} \left(9 \log{\left(x \right)}^{6} - 9 \log{\left(x \right)}^{4} + 18 \log{\left(x \right)}^{3} + 2 \log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 2\right)}{x^{3}}
Gráfico
Derivada de x^ln^2x