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y=sqrt(|3x+2|-|x-1|)
Derivada de la función/ |x-1|/ y=sqrt(|3x+2|-|x-1|)

Derivada de y=sqrt(|3x+2|-|x-1|)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
  _____________________
\/ |3*x + 2| - |x - 1|
−∣x−1∣+∣3x+2∣\sqrt{- \left|{x - 1}\right| + \left|{3 x + 2}\right|} 
sqrt(|3*x + 2| - |x - 1|)
Gráfica
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
  sign(-1 + x)   3*sign(2 + 3*x)
- ------------ + ---------------
       2                2       
--------------------------------
      _____________________     
    \/ |3*x + 2| - |x - 1|
−sign⁡(x−1)2+3sign⁡(3x+2)2−∣x−1∣+∣3x+2∣\frac{- \frac{\operatorname{sign}{\left(x - 1 \right)}}{2} + \frac{3 \operatorname{sign}{\left(3 x + 2 \right)}}{2}}{\sqrt{- \left|{x - 1}\right| + \left|{3 x + 2}\right|}}
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Segunda derivada [src] 
 /                                                          2                     \ 
 |                         (-3*sign(2 + 3*x) + sign(-1 + x))                      | 
-|-9*DiracDelta(2 + 3*x) + ---------------------------------- + DiracDelta(-1 + x)| 
 \                             4*(-|-1 + x| + |2 + 3*x|)                          / 
------------------------------------------------------------------------------------
                               _______________________                              
                             \/ -|-1 + x| + |2 + 3*x|
−δ(x−1)−9δ(3x+2)+(sign⁡(x−1)−3sign⁡(3x+2))24(−∣x−1∣+∣3x+2∣)−∣x−1∣+∣3x+2∣- \frac{\delta\left(x - 1\right) - 9 \delta\left(3 x + 2\right) + \frac{\left(\operatorname{sign}{\left(x - 1 \right)} - 3 \operatorname{sign}{\left(3 x + 2 \right)}\right)^{2}}{4 \left(- \left|{x - 1}\right| + \left|{3 x + 2}\right|\right)}}{\sqrt{- \left|{x - 1}\right| + \left|{3 x + 2}\right|}}
Simplificar
Tercera derivada [src] 
 /                                                                3                                                                                                            \ 
 |                             3*(-3*sign(2 + 3*x) + sign(-1 + x))    3*(-9*DiracDelta(2 + 3*x) + DiracDelta(-1 + x))*(-3*sign(2 + 3*x) + sign(-1 + x))                        | 
-|-27*DiracDelta(2 + 3*x, 1) + ------------------------------------ + --------------------------------------------------------------------------------- + DiracDelta(-1 + x, 1)| 
 |                                                           2                                    2*(-|-1 + x| + |2 + 3*x|)                                                    | 
 \                                  8*(-|-1 + x| + |2 + 3*x|)                                                                                                                  / 
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                              _______________________                                                                            
                                                                            \/ -|-1 + x| + |2 + 3*x|
−δ(1)(x−1)−27δ(1)(3x+2)+3(δ(x−1)−9δ(3x+2))(sign⁡(x−1)−3sign⁡(3x+2))2(−∣x−1∣+∣3x+2∣)+3(sign⁡(x−1)−3sign⁡(3x+2))38(−∣x−1∣+∣3x+2∣)2−∣x−1∣+∣3x+2∣- \frac{\delta^{\left( 1 \right)}\left( x - 1 \right) - 27 \delta^{\left( 1 \right)}\left( 3 x + 2 \right) + \frac{3 \left(\delta\left(x - 1\right) - 9 \delta\left(3 x + 2\right)\right) \left(\operatorname{sign}{\left(x - 1 \right)} - 3 \operatorname{sign}{\left(3 x + 2 \right)}\right)}{2 \left(- \left|{x - 1}\right| + \left|{3 x + 2}\right|\right)} + \frac{3 \left(\operatorname{sign}{\left(x - 1 \right)} - 3 \operatorname{sign}{\left(3 x + 2 \right)}\right)^{3}}{8 \left(- \left|{x - 1}\right| + \left|{3 x + 2}\right|\right)^{2}}}{\sqrt{- \left|{x - 1}\right| + \left|{3 x + 2}\right|}}
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Gráfico
Derivada de y=sqrt(|3x+2|-|x-1|)
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