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x^(lnx+1)
Derivada de la función/ lnx+1/ x^(lnx+1)

Derivada de x^(lnx+1)

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

Ha introducido [src] 
 log(x) + 1
x
xlog⁡(x)+1x^{\log{\left(x \right)} + 1} 
x^(log(x) + 1)
Solución detallada

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

    Perola derivada

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

  2. Simplificamos:

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-25002500
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 log(x) + 1 /log(x) + 1   log(x)\
x          *|---------- + ------|
            \    x          x   /
xlog⁡(x)+1(log⁡(x)+1x+log⁡(x)x)x^{\log{\left(x \right)} + 1} \left(\frac{\log{\left(x \right)} + 1}{x} + \frac{\log{\left(x \right)}}{x}\right)
Simplificar
Segunda derivada [src] 
 1 + log(x) /                  2           \
x          *\1 + (1 + 2*log(x))  - 2*log(x)/
--------------------------------------------
                      2                     
                     x
xlog⁡(x)+1((2log⁡(x)+1)2−2log⁡(x)+1)x2\frac{x^{\log{\left(x \right)} + 1} \left(\left(2 \log{\left(x \right)} + 1\right)^{2} - 2 \log{\left(x \right)} + 1\right)}{x^{2}}
Simplificar
Tercera derivada [src] 
 1 + log(x) /                   3                                              \
x          *\-4 + (1 + 2*log(x))  + 4*log(x) - 3*(1 + 2*log(x))*(-1 + 2*log(x))/
--------------------------------------------------------------------------------
                                        3                                       
                                       x
xlog⁡(x)+1(−3(2log⁡(x)−1)(2log⁡(x)+1)+(2log⁡(x)+1)3+4log⁡(x)−4)x3\frac{x^{\log{\left(x \right)} + 1} \left(- 3 \left(2 \log{\left(x \right)} - 1\right) \left(2 \log{\left(x \right)} + 1\right) + \left(2 \log{\left(x \right)} + 1\right)^{3} + 4 \log{\left(x \right)} - 4\right)}{x^{3}}
Simplificar
Gráfico
Derivada de x^(lnx+1)
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