Sr Examen

Derivada de |x|*exp(|x|)

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

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Solución

Ha introducido [src]
     |x|
|x|*e   
$$e^{\left|{x}\right|} \left|{x}\right|$$
|x|*exp(|x|)
Gráfica
Primera derivada [src]
 |x|                |x|        
e   *sign(x) + |x|*e   *sign(x)
$$e^{\left|{x}\right|} \left|{x}\right| \operatorname{sign}{\left(x \right)} + e^{\left|{x}\right|} \operatorname{sign}{\left(x \right)}$$
Segunda derivada [src]
/      2                        /    2                     \    \  |x|
\2*sign (x) + 2*DiracDelta(x) + \sign (x) + 2*DiracDelta(x)/*|x|/*e   
$$\left(\left(2 \delta\left(x\right) + \operatorname{sign}^{2}{\left(x \right)}\right) \left|{x}\right| + 2 \delta\left(x\right) + 2 \operatorname{sign}^{2}{\left(x \right)}\right) e^{\left|{x}\right|}$$
Tercera derivada [src]
/                     /    3                                                  \         /    2                     \                                  \  |x|
\2*DiracDelta(x, 1) + \sign (x) + 2*DiracDelta(x, 1) + 6*DiracDelta(x)*sign(x)/*|x| + 3*\sign (x) + 2*DiracDelta(x)/*sign(x) + 6*DiracDelta(x)*sign(x)/*e   
$$\left(3 \left(2 \delta\left(x\right) + \operatorname{sign}^{2}{\left(x \right)}\right) \operatorname{sign}{\left(x \right)} + \left(6 \delta\left(x\right) \operatorname{sign}{\left(x \right)} + 2 \delta^{\left( 1 \right)}\left( x \right) + \operatorname{sign}^{3}{\left(x \right)}\right) \left|{x}\right| + 6 \delta\left(x\right) \operatorname{sign}{\left(x \right)} + 2 \delta^{\left( 1 \right)}\left( x \right)\right) e^{\left|{x}\right|}$$
Gráfico
Derivada de |x|*exp(|x|)