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Derivada de la función/ |x-1|/ |x|*e^(-|x-1|)

Derivada de |x|*e^(-|x-1|)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     -|x - 1|
|x|*E
e−∣x−1∣∣x∣e^{- \left|{x - 1}\right|} \left|{x}\right| 
|x|*E^(-|x - 1|)
Primera derivada [src] 
 -|x - 1|                -|x - 1|             
e        *sign(x) - |x|*e        *sign(-1 + x)
−e−∣x−1∣∣x∣sign⁡(x−1)+e−∣x−1∣sign⁡(x)- e^{- \left|{x - 1}\right|} \left|{x}\right| \operatorname{sign}{\left(x - 1 \right)} + e^{- \left|{x - 1}\right|} \operatorname{sign}{\left(x \right)}
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Segunda derivada [src] 
/                  /      2                               \                             \  -|-1 + x|
\2*DiracDelta(x) - \- sign (-1 + x) + 2*DiracDelta(-1 + x)/*|x| - 2*sign(x)*sign(-1 + x)/*e
(−(2δ(x−1)−sign⁡2(x−1))∣x∣+2δ(x)−2sign⁡(x)sign⁡(x−1))e−∣x−1∣\left(- \left(2 \delta\left(x - 1\right) - \operatorname{sign}^{2}{\left(x - 1 \right)}\right) \left|{x}\right| + 2 \delta\left(x\right) - 2 \operatorname{sign}{\left(x \right)} \operatorname{sign}{\left(x - 1 \right)}\right) e^{- \left|{x - 1}\right|}
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Tercera derivada [src] 
/                     /    3                                                                      \                                        /      2                               \        \  -|-1 + x|
\2*DiracDelta(x, 1) - \sign (-1 + x) + 2*DiracDelta(-1 + x, 1) - 6*DiracDelta(-1 + x)*sign(-1 + x)/*|x| - 6*DiracDelta(x)*sign(-1 + x) - 3*\- sign (-1 + x) + 2*DiracDelta(-1 + x)/*sign(x)/*e
(−3(2δ(x−1)−sign⁡2(x−1))sign⁡(x)−(−6δ(x−1)sign⁡(x−1)+2δ(1)(x−1)+sign⁡3(x−1))∣x∣−6δ(x)sign⁡(x−1)+2δ(1)(x))e−∣x−1∣\left(- 3 \left(2 \delta\left(x - 1\right) - \operatorname{sign}^{2}{\left(x - 1 \right)}\right) \operatorname{sign}{\left(x \right)} - \left(- 6 \delta\left(x - 1\right) \operatorname{sign}{\left(x - 1 \right)} + 2 \delta^{\left( 1 \right)}\left( x - 1 \right) + \operatorname{sign}^{3}{\left(x - 1 \right)}\right) \left|{x}\right| - 6 \delta\left(x\right) \operatorname{sign}{\left(x - 1 \right)} + 2 \delta^{\left( 1 \right)}\left( x \right)\right) e^{- \left|{x - 1}\right|}
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