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lnx^x
Derivada de la función/ lnx^x

Derivada de lnx^x

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

Gráfico:

interior superior

Definida a trozos:

Solución

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

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010010000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   x    /  1                 \
log (x)*|------ + log(log(x))|
        \log(x)              /
(log⁡(log⁡(x))+1log⁡(x))log⁡(x)x\left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x}
Simplificar
Segunda derivada [src] 
        /                                1   \
        |                      2   1 - ------|
   x    |/  1                 \        log(x)|
log (x)*||------ + log(log(x))|  + ----------|
        \\log(x)              /     x*log(x) /
((log⁡(log⁡(x))+1log⁡(x))2+1−1log⁡(x)xlog⁡(x))log⁡(x)x\left(\left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} + \frac{1 - \frac{1}{\log{\left(x \right)}}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{x}
Simplificar
Tercera derivada [src] 
        /                                 2                                           \
        |                          1 - -------     /      1   \ /  1                 \|
        |                      3          2      3*|1 - ------|*|------ + log(log(x))||
   x    |/  1                 \        log (x)     \    log(x)/ \log(x)              /|
log (x)*||------ + log(log(x))|  - ----------- + -------------------------------------|
        |\log(x)              /      2                          x*log(x)              |
        \                           x *log(x)                                         /
((log⁡(log⁡(x))+1log⁡(x))3+3(1−1log⁡(x))(log⁡(log⁡(x))+1log⁡(x))xlog⁡(x)−1−2log⁡(x)2x2log⁡(x))log⁡(x)x\left(\left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{3} + \frac{3 \left(1 - \frac{1}{\log{\left(x \right)}}\right) \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)}{x \log{\left(x \right)}} - \frac{1 - \frac{2}{\log{\left(x \right)}^{2}}}{x^{2} \log{\left(x \right)}}\right) \log{\left(x \right)}^{x}
Simplificar
Gráfico
Derivada de lnx^x
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