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

Derivada de (x+lnx)^x

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

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Solución

Ha introducido [src] 
            x
(x + log(x))
(x+log⁡(x))x\left(x + \log{\left(x \right)}\right)^{x} 
(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
02468-8-6-4-2-10100500000000000
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Primera derivada [src] 
              /  /    1\                   \
              |x*|1 + -|                   |
            x |  \    x/                   |
(x + log(x)) *|---------- + log(x + log(x))|
              \x + log(x)                  /
(x+log⁡(x))x(x(1+1x)x+log⁡(x)+log⁡(x+log⁡(x)))\left(x + \log{\left(x \right)}\right)^{x} \left(\frac{x \left(1 + \frac{1}{x}\right)}{x + \log{\left(x \right)}} + \log{\left(x + \log{\left(x \right)} \right)}\right)
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Segunda derivada [src] 
              /                                                    2\
              |                                             /    1\ |
              |                              2            x*|1 + -| |
              |/  /    1\                   \         1     \    x/ |
              ||x*|1 + -|                   |    -2 - - + ----------|
            x ||  \    x/                   |         x   x + log(x)|
(x + log(x)) *||---------- + log(x + log(x))|  - -------------------|
              \\x + log(x)                  /         x + log(x)    /
(x+log⁡(x))x((x(1+1x)x+log⁡(x)+log⁡(x+log⁡(x)))2−x(1+1x)2x+log⁡(x)−2−1xx+log⁡(x))\left(x + \log{\left(x \right)}\right)^{x} \left(\left(\frac{x \left(1 + \frac{1}{x}\right)}{x + \log{\left(x \right)}} + \log{\left(x + \log{\left(x \right)} \right)}\right)^{2} - \frac{\frac{x \left(1 + \frac{1}{x}\right)^{2}}{x + \log{\left(x \right)}} - 2 - \frac{1}{x}}{x + \log{\left(x \right)}}\right)
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Tercera derivada [src] 
              /                                                  2               3                                                                          \
              |                                           /    1\         /    1\        /    1\                                       /                  2\|
              |                                         3*|1 + -|     2*x*|1 + -|      3*|1 + -|        /  /    1\                   \ |           /    1\ ||
              |                              3     1      \    x/         \    x/        \    x/        |x*|1 + -|                   | |         x*|1 + -| ||
              |/  /    1\                   \    - -- - ---------- + ------------- + --------------     |  \    x/                   | |     1     \    x/ ||
              ||x*|1 + -|                   |       2   x + log(x)               2   x*(x + log(x))   3*|---------- + log(x + log(x))|*|-2 - - + ----------||
            x ||  \    x/                   |      x                 (x + log(x))                       \x + log(x)                  / \     x   x + log(x)/|
(x + log(x)) *||---------- + log(x + log(x))|  + -------------------------------------------------- - ------------------------------------------------------|
              \\x + log(x)                  /                        x + log(x)                                             x + log(x)                      /
(x+log⁡(x))x((x(1+1x)x+log⁡(x)+log⁡(x+log⁡(x)))3−3(x(1+1x)x+log⁡(x)+log⁡(x+log⁡(x)))(x(1+1x)2x+log⁡(x)−2−1x)x+log⁡(x)+2x(1+1x)3(x+log⁡(x))2−3(1+1x)2x+log⁡(x)+3(1+1x)x(x+log⁡(x))−1x2x+log⁡(x))\left(x + \log{\left(x \right)}\right)^{x} \left(\left(\frac{x \left(1 + \frac{1}{x}\right)}{x + \log{\left(x \right)}} + \log{\left(x + \log{\left(x \right)} \right)}\right)^{3} - \frac{3 \left(\frac{x \left(1 + \frac{1}{x}\right)}{x + \log{\left(x \right)}} + \log{\left(x + \log{\left(x \right)} \right)}\right) \left(\frac{x \left(1 + \frac{1}{x}\right)^{2}}{x + \log{\left(x \right)}} - 2 - \frac{1}{x}\right)}{x + \log{\left(x \right)}} + \frac{\frac{2 x \left(1 + \frac{1}{x}\right)^{3}}{\left(x + \log{\left(x \right)}\right)^{2}} - \frac{3 \left(1 + \frac{1}{x}\right)^{2}}{x + \log{\left(x \right)}} + \frac{3 \left(1 + \frac{1}{x}\right)}{x \left(x + \log{\left(x \right)}\right)} - \frac{1}{x^{2}}}{x + \log{\left(x \right)}}\right)
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Gráfico
Derivada de (x+lnx)^x
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