Sr Examen

Derivada de log(|x|)

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

Gráfico:

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Solución

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