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Derivada de la función/ (|x|)/ (|x|)^(x)

Derivada de (|x|)^(x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   x
|x|
$$\left|{x}\right|^{x}$$ 
|x|^x
Solución detallada

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

    Perola derivada

Respuesta:

Primera derivada [src] 
   x /x*sign(x)           \
|x| *|--------- + log(|x|)|
     \   |x|              /
$$\left(\frac{x \operatorname{sign}{\left(x \right)}}{\left|{x}\right|} + \log{\left(\left|{x}\right| \right)}\right) \left|{x}\right|^{x}$$
Simplificar
Segunda derivada [src] 
     /                      2       2                                   \
   x |/x*sign(x)           \    sign (x)   2*sign(x)   2*x*DiracDelta(x)|
|x| *||--------- + log(|x|)|  - -------- + --------- + -----------------|
     \\   |x|              /       x          |x|             |x|       /
$$\left(\frac{2 x \delta\left(x\right)}{\left|{x}\right|} + \left(\frac{x \operatorname{sign}{\left(x \right)}}{\left|{x}\right|} + \log{\left(\left|{x}\right| \right)}\right)^{2} + \frac{2 \operatorname{sign}{\left(x \right)}}{\left|{x}\right|} - \frac{\operatorname{sign}^{2}{\left(x \right)}}{x}\right) \left|{x}\right|^{x}$$
Simplificar
Tercera derivada [src] 
     /                      3       2                               /      2                                   \                                                                   \
   x |/x*sign(x)           \    sign (x)     /x*sign(x)           \ |  sign (x)   2*sign(x)   2*x*DiracDelta(x)|   6*DiracDelta(x)   6*DiracDelta(x)*sign(x)   2*x*DiracDelta(x, 1)|
|x| *||--------- + log(|x|)|  - -------- + 3*|--------- + log(|x|)|*|- -------- + --------- + -----------------| + --------------- - ----------------------- + --------------------|
     |\   |x|              /        2        \   |x|              / \     x          |x|             |x|       /         |x|                    x                      |x|         |
     \                             x                                                                                                                                               /
$$\left(\frac{2 x \delta^{\left( 1 \right)}\left( x \right)}{\left|{x}\right|} + \left(\frac{x \operatorname{sign}{\left(x \right)}}{\left|{x}\right|} + \log{\left(\left|{x}\right| \right)}\right)^{3} + 3 \left(\frac{x \operatorname{sign}{\left(x \right)}}{\left|{x}\right|} + \log{\left(\left|{x}\right| \right)}\right) \left(\frac{2 x \delta\left(x\right)}{\left|{x}\right|} + \frac{2 \operatorname{sign}{\left(x \right)}}{\left|{x}\right|} - \frac{\operatorname{sign}^{2}{\left(x \right)}}{x}\right) + \frac{6 \delta\left(x\right)}{\left|{x}\right|} - \frac{6 \delta\left(x\right) \operatorname{sign}{\left(x \right)}}{x} - \frac{\operatorname{sign}^{2}{\left(x \right)}}{x^{2}}\right) \left|{x}\right|^{x}$$
Simplificar
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