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Derivada de la función/ x*exp/ abs(x)/ x*exp(-n*abs(x))/abs(x)

Derivada de x*exp(-n*abs(x))/abs(x)

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

Gráfico:

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Solución

Ha introducido [src] 
   -n*|x|
x*e      
---------
   |x|
xe−n∣x∣∣x∣\frac{x e^{- n \left|{x}\right|}}{\left|{x}\right|} 
(x*exp((-n)*|x|))/|x|
Primera derivada [src] 
       -n*|x|            -n*|x|    -n*|x|        
- n*x*e      *sign(x) + e         e      *sign(x)
------------------------------- - ---------------
              |x|                        x
−nxe−n∣x∣sign⁡(x)+e−n∣x∣∣x∣−e−n∣x∣sign⁡(x)x\frac{- n x e^{- n \left|{x}\right|} \operatorname{sign}{\left(x \right)} + e^{- n \left|{x}\right|}}{\left|{x}\right|} - \frac{e^{- n \left|{x}\right|} \operatorname{sign}{\left(x \right)}}{x}
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Segunda derivada [src] 
/    /  sign(x)                \                                                                                    \        
|  2*|- ------- + DiracDelta(x)|     /               /                         2   \\                               |        
|    \     x                   /   n*\-2*sign(x) + x*\-2*DiracDelta(x) + n*sign (x)//   2*(-1 + n*x*sign(x))*sign(x)|  -n*|x|
|- ----------------------------- + -------------------------------------------------- + ----------------------------|*e      
|                x                                        |x|                                         2             |        
\                                                                                                    x              /
(n(x(nsign⁡2(x)−2δ(x))−2sign⁡(x))∣x∣−2(δ(x)−sign⁡(x)x)x+2(nxsign⁡(x)−1)sign⁡(x)x2)e−n∣x∣\left(\frac{n \left(x \left(n \operatorname{sign}^{2}{\left(x \right)} - 2 \delta\left(x\right)\right) - 2 \operatorname{sign}{\left(x \right)}\right)}{\left|{x}\right|} - \frac{2 \left(\delta\left(x\right) - \frac{\operatorname{sign}{\left(x \right)}}{x}\right)}{x} + \frac{2 \left(n x \operatorname{sign}{\left(x \right)} - 1\right) \operatorname{sign}{\left(x \right)}}{x^{2}}\right) e^{- n \left|{x}\right|}
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Tercera derivada [src] 
/    /  4*DiracDelta(x)   3*sign(x)                   \                                                                                                                                                                                                                          \        
|  2*|- --------------- + --------- + DiracDelta(x, 1)|                                                                                                                                /  sign(x)                \                                                               |        
|    |         x               2                      |     /                    /                      2     3                               \           2   \   6*(-1 + n*x*sign(x))*|- ------- + DiracDelta(x)|       /               /                         2   \\        |        
|    \                        x                       /   n*\6*DiracDelta(x) + x*\2*DiracDelta(x, 1) + n *sign (x) - 6*n*DiracDelta(x)*sign(x)/ - 3*n*sign (x)/                        \     x                   /   3*n*\-2*sign(x) + x*\-2*DiracDelta(x) + n*sign (x)//*sign(x)|  -n*|x|
|- ---------------------------------------------------- - ----------------------------------------------------------------------------------------------------- + ------------------------------------------------ - ------------------------------------------------------------|*e      
|                           x                                                                              |x|                                                                            2                                                        2                             |        
\                                                                                                                                                                                        x                                                        x                              /
(−n(−3nsign⁡2(x)+x(n2sign⁡3(x)−6nδ(x)sign⁡(x)+2δ(1)(x))+6δ(x))∣x∣−3n(x(nsign⁡2(x)−2δ(x))−2sign⁡(x))sign⁡(x)x2−2(δ(1)(x)−4δ(x)x+3sign⁡(x)x2)x+6(nxsign⁡(x)−1)(δ(x)−sign⁡(x)x)x2)e−n∣x∣\left(- \frac{n \left(- 3 n \operatorname{sign}^{2}{\left(x \right)} + x \left(n^{2} \operatorname{sign}^{3}{\left(x \right)} - 6 n \delta\left(x\right) \operatorname{sign}{\left(x \right)} + 2 \delta^{\left( 1 \right)}\left( x \right)\right) + 6 \delta\left(x\right)\right)}{\left|{x}\right|} - \frac{3 n \left(x \left(n \operatorname{sign}^{2}{\left(x \right)} - 2 \delta\left(x\right)\right) - 2 \operatorname{sign}{\left(x \right)}\right) \operatorname{sign}{\left(x \right)}}{x^{2}} - \frac{2 \left(\delta^{\left( 1 \right)}\left( x \right) - \frac{4 \delta\left(x\right)}{x} + \frac{3 \operatorname{sign}{\left(x \right)}}{x^{2}}\right)}{x} + \frac{6 \left(n x \operatorname{sign}{\left(x \right)} - 1\right) \left(\delta\left(x\right) - \frac{\operatorname{sign}{\left(x \right)}}{x}\right)}{x^{2}}\right) e^{- n \left|{x}\right|}
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