Sr Examen

Derivada de (|x|/x²)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
|x|
---
  2
 x 
$$\frac{\left|{x}\right|}{x^{2}}$$
|x|/x^2
Primera derivada [src]
sign(x)   2*|x|
------- - -----
    2        3 
   x        x  
$$\frac{\operatorname{sign}{\left(x \right)}}{x^{2}} - \frac{2 \left|{x}\right|}{x^{3}}$$
Segunda derivada [src]
  /  2*sign(x)   3*|x|                \
2*|- --------- + ----- + DiracDelta(x)|
  |      x          2                 |
  \                x                  /
---------------------------------------
                    2                  
                   x                   
$$\frac{2 \left(\delta\left(x\right) - \frac{2 \operatorname{sign}{\left(x \right)}}{x} + \frac{3 \left|{x}\right|}{x^{2}}\right)}{x^{2}}$$
Tercera derivada [src]
  /  12*|x|   6*DiracDelta(x)   9*sign(x)                   \
2*|- ------ - --------------- + --------- + DiracDelta(x, 1)|
  |     3            x               2                      |
  \    x                            x                       /
-------------------------------------------------------------
                               2                             
                              x                              
$$\frac{2 \left(\delta^{\left( 1 \right)}\left( x \right) - \frac{6 \delta\left(x\right)}{x} + \frac{9 \operatorname{sign}{\left(x \right)}}{x^{2}} - \frac{12 \left|{x}\right|}{x^{3}}\right)}{x^{2}}$$