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|x|/|x-2|
Derivada de la función/ |x-2|/ |x|/|x-2|

Derivada de |x|/|x-2|

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

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Solución

Ha introducido [src] 
  |x|  
-------
|x - 2|
∣x∣∣x−2∣\frac{\left|{x}\right|}{\left|{x - 2}\right|} 
|x|/|x - 2|
Gráfica
02468-8-6-4-2-1010-250250
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
sign(x)   |x|*sign(-2 + x)
------- - ----------------
|x - 2|              2    
              (x - 2)
sign⁡(x)∣x−2∣−∣x∣sign⁡(x−2)(x−2)2\frac{\operatorname{sign}{\left(x \right)}}{\left|{x - 2}\right|} - \frac{\left|{x}\right| \operatorname{sign}{\left(x - 2 \right)}}{\left(x - 2\right)^{2}}
Simplificar
Segunda derivada [src] 
  /                /  sign(-2 + x)                     \                           \
  |                |- ------------ + DiracDelta(-2 + x)|*|x|                       |
  |DiracDelta(x)   \     -2 + x                        /       sign(x)*sign(-2 + x)|
2*|------------- - ----------------------------------------- - --------------------|
  |   |-2 + x|                             2                                2      |
  \                                (-2 + x)                         (-2 + x)       /
2(δ(x)∣x−2∣−(δ(x−2)−sign⁡(x−2)x−2)∣x∣(x−2)2−sign⁡(x)sign⁡(x−2)(x−2)2)2 \left(\frac{\delta\left(x\right)}{\left|{x - 2}\right|} - \frac{\left(\delta\left(x - 2\right) - \frac{\operatorname{sign}{\left(x - 2 \right)}}{x - 2}\right) \left|{x}\right|}{\left(x - 2\right)^{2}} - \frac{\operatorname{sign}{\left(x \right)} \operatorname{sign}{\left(x - 2 \right)}}{\left(x - 2\right)^{2}}\right)
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Tercera derivada [src] 
  /                   /  4*DiracDelta(-2 + x)   3*sign(-2 + x)                        \                                                                                     \
  |                   |- -------------------- + -------------- + DiracDelta(-2 + x, 1)|*|x|     /  sign(-2 + x)                     \                                       |
  |                   |         -2 + x                    2                           |       3*|- ------------ + DiracDelta(-2 + x)|*sign(x)                               |
  |DiracDelta(x, 1)   \                           (-2 + x)                            /         \     -2 + x                        /           3*DiracDelta(x)*sign(-2 + x)|
2*|---------------- - --------------------------------------------------------------------- - ----------------------------------------------- - ----------------------------|
  |    |-2 + x|                                             2                                                            2                                       2          |
  \                                                 (-2 + x)                                                     (-2 + x)                                (-2 + x)           /
2(δ(1)(x)∣x−2∣−3(δ(x−2)−sign⁡(x−2)x−2)sign⁡(x)(x−2)2−(δ(1)(x−2)−4δ(x−2)x−2+3sign⁡(x−2)(x−2)2)∣x∣(x−2)2−3δ(x)sign⁡(x−2)(x−2)2)2 \left(\frac{\delta^{\left( 1 \right)}\left( x \right)}{\left|{x - 2}\right|} - \frac{3 \left(\delta\left(x - 2\right) - \frac{\operatorname{sign}{\left(x - 2 \right)}}{x - 2}\right) \operatorname{sign}{\left(x \right)}}{\left(x - 2\right)^{2}} - \frac{\left(\delta^{\left( 1 \right)}\left( x - 2 \right) - \frac{4 \delta\left(x - 2\right)}{x - 2} + \frac{3 \operatorname{sign}{\left(x - 2 \right)}}{\left(x - 2\right)^{2}}\right) \left|{x}\right|}{\left(x - 2\right)^{2}} - \frac{3 \delta\left(x\right) \operatorname{sign}{\left(x - 2 \right)}}{\left(x - 2\right)^{2}}\right)
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Gráfico
Derivada de |x|/|x-2|
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