Sr Examen

Derivada de ln(1+|x|)

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

Gráfico:

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Solución

Ha introducido [src]
log(1 + |x|)
log(x+1)\log{\left(\left|{x}\right| + 1 \right)}
log(1 + |x|)
Gráfica
02468-8-6-4-2-10105-5
Primera derivada [src]
sign(x)
-------
1 + |x|
sign(x)x+1\frac{\operatorname{sign}{\left(x \right)}}{\left|{x}\right| + 1}
Segunda derivada [src]
                      2   
                  sign (x)
2*DiracDelta(x) - --------
                  1 + |x| 
--------------------------
         1 + |x|          
2δ(x)sign2(x)x+1x+1\frac{2 \delta\left(x\right) - \frac{\operatorname{sign}^{2}{\left(x \right)}}{\left|{x}\right| + 1}}{\left|{x}\right| + 1}
Tercera derivada [src]
  /     3                                                 \
  | sign (x)    3*DiracDelta(x)*sign(x)                   |
2*|---------- - ----------------------- + DiracDelta(x, 1)|
  |         2           1 + |x|                           |
  \(1 + |x|)                                              /
-----------------------------------------------------------
                          1 + |x|                          
2(δ(1)(x)3δ(x)sign(x)x+1+sign3(x)(x+1)2)x+1\frac{2 \left(\delta^{\left( 1 \right)}\left( x \right) - \frac{3 \delta\left(x\right) \operatorname{sign}{\left(x \right)}}{\left|{x}\right| + 1} + \frac{\operatorname{sign}^{3}{\left(x \right)}}{\left(\left|{x}\right| + 1\right)^{2}}\right)}{\left|{x}\right| + 1}
Gráfico
Derivada de ln(1+|x|)