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

Derivada de x^(x+lnx)

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

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

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-1000000000000010000000000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 x + log(x) /x + log(x)   /    1\       \
x          *|---------- + |1 + -|*log(x)|
            \    x        \    x/       /
xx+log⁡(x)((1+1x)log⁡(x)+x+log⁡(x)x)x^{x + \log{\left(x \right)}} \left(\left(1 + \frac{1}{x}\right) \log{\left(x \right)} + \frac{x + \log{\left(x \right)}}{x}\right)
Simplificar
Segunda derivada [src] 
            /                                      2   x + log(x)   log(x)\
            |                             2   -2 - - + ---------- + ------|
 x + log(x) |/x + log(x)   /    1\       \         x       x          x   |
x          *||---------- + |1 + -|*log(x)|  - ----------------------------|
            \\    x        \    x/       /                 x              /
xx+log⁡(x)(((1+1x)log⁡(x)+x+log⁡(x)x)2−−2+x+log⁡(x)x+log⁡(x)x−2xx)x^{x + \log{\left(x \right)}} \left(\left(\left(1 + \frac{1}{x}\right) \log{\left(x \right)} + \frac{x + \log{\left(x \right)}}{x}\right)^{2} - \frac{-2 + \frac{x + \log{\left(x \right)}}{x} + \frac{\log{\left(x \right)}}{x} - \frac{2}{x}}{x}\right)
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Tercera derivada [src] 
            /                                     6   2*(x + log(x))   2*log(x)     /x + log(x)   /    1\       \ /     2   x + log(x)   log(x)\\
            |                             3   3 + - - -------------- - --------   3*|---------- + |1 + -|*log(x)|*|-2 - - + ---------- + ------||
 x + log(x) |/x + log(x)   /    1\       \        x         x             x         \    x        \    x/       / \     x       x          x   /|
x          *||---------- + |1 + -|*log(x)|  - --------------------------------- - --------------------------------------------------------------|
            |\    x        \    x/       /                     2                                                x                               |
            \                                                 x                                                                                 /
xx+log⁡(x)(((1+1x)log⁡(x)+x+log⁡(x)x)3−3((1+1x)log⁡(x)+x+log⁡(x)x)(−2+x+log⁡(x)x+log⁡(x)x−2x)x−3−2(x+log⁡(x))x−2log⁡(x)x+6xx2)x^{x + \log{\left(x \right)}} \left(\left(\left(1 + \frac{1}{x}\right) \log{\left(x \right)} + \frac{x + \log{\left(x \right)}}{x}\right)^{3} - \frac{3 \left(\left(1 + \frac{1}{x}\right) \log{\left(x \right)} + \frac{x + \log{\left(x \right)}}{x}\right) \left(-2 + \frac{x + \log{\left(x \right)}}{x} + \frac{\log{\left(x \right)}}{x} - \frac{2}{x}\right)}{x} - \frac{3 - \frac{2 \left(x + \log{\left(x \right)}\right)}{x} - \frac{2 \log{\left(x \right)}}{x} + \frac{6}{x}}{x^{2}}\right)
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Gráfico
Derivada de x^(x+lnx)
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