Sr Examen

Derivada de x*exp(sign(x))

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

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Solución

Ha introducido [src]
   sign(x)
x*e       
xesign(x)x e^{\operatorname{sign}{\left(x \right)}}
x*exp(sign(x))
Gráfica
02468-8-6-4-2-1010-5050
Primera derivada [src]
                   sign(x)    sign(x)
2*x*DiracDelta(x)*e        + e       
2xesign(x)δ(x)+esign(x)2 x e^{\operatorname{sign}{\left(x \right)}} \delta\left(x\right) + e^{\operatorname{sign}{\left(x \right)}}
Segunda derivada [src]
  /                    /            2                      \\  sign(x)
2*\2*DiracDelta(x) + x*\2*DiracDelta (x) + DiracDelta(x, 1)//*e       
2(x(2(δ(x))2+δ(1)(x))+2δ(x))esign(x)2 \left(x \left(2 \left(\delta\left(x\right)\right)^{2} + \delta^{\left( 1 \right)}\left( x \right)\right) + 2 \delta\left(x\right)\right) e^{\operatorname{sign}{\left(x \right)}}
Tercera derivada [src]
  /                                 2        /            3                                                         \\  sign(x)
2*\3*DiracDelta(x, 1) + 6*DiracDelta (x) + x*\4*DiracDelta (x) + 6*DiracDelta(x)*DiracDelta(x, 1) + DiracDelta(x, 2)//*e       
2(x(4(δ(x))3+6δ(x)δ(1)(x)+δ(2)(x))+6(δ(x))2+3δ(1)(x))esign(x)2 \left(x \left(4 \left(\delta\left(x\right)\right)^{3} + 6 \delta\left(x\right) \delta^{\left( 1 \right)}\left( x \right) + \delta^{\left( 2 \right)}\left( x \right)\right) + 6 \left(\delta\left(x\right)\right)^{2} + 3 \delta^{\left( 1 \right)}\left( x \right)\right) e^{\operatorname{sign}{\left(x \right)}}
Gráfico
Derivada de x*exp(sign(x))