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Derivada de la función/ (x-1)/ |x|/(x-1)^2

Derivada de |x|/(x-1)^2

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Solución

Ha introducido [src] 
  |x|   
--------
       2
(x - 1)
$$\frac{\left|{x}\right|}{\left(x - 1\right)^{2}}$$ 
|x|/(x - 1)^2
Primera derivada [src] 
sign(x)    (2 - 2*x)*|x|
-------- + -------------
       2             4  
(x - 1)       (x - 1)
$$\frac{\left(2 - 2 x\right) \left|{x}\right|}{\left(x - 1\right)^{4}} + \frac{\operatorname{sign}{\left(x \right)}}{\left(x - 1\right)^{2}}$$
Simplificar
Segunda derivada [src] 
  /  2*sign(x)     3*|x|                  \
2*|- --------- + --------- + DiracDelta(x)|
  |    -1 + x            2                |
  \              (-1 + x)                 /
-------------------------------------------
                         2                 
                 (-1 + x)
$$\frac{2 \left(\delta\left(x\right) - \frac{2 \operatorname{sign}{\left(x \right)}}{x - 1} + \frac{3 \left|{x}\right|}{\left(x - 1\right)^{2}}\right)}{\left(x - 1\right)^{2}}$$
Simplificar
Tercera derivada [src] 
  /    12*|x|    6*DiracDelta(x)   9*sign(x)                   \
2*|- --------- - --------------- + --------- + DiracDelta(x, 1)|
  |          3        -1 + x               2                   |
  \  (-1 + x)                      (-1 + x)                    /
----------------------------------------------------------------
                                   2                            
                           (-1 + x)
$$\frac{2 \left(\delta^{\left( 1 \right)}\left( x \right) - \frac{6 \delta\left(x\right)}{x - 1} + \frac{9 \operatorname{sign}{\left(x \right)}}{\left(x - 1\right)^{2}} - \frac{12 \left|{x}\right|}{\left(x - 1\right)^{3}}\right)}{\left(x - 1\right)^{2}}$$
Simplificar
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