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Derivada de la función/ x^2+2/ |x|/(x^2+23)

Derivada de |x|/(x^2+23)

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

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Solución

Ha introducido [src] 
  |x|  
-------
 2     
x  + 23
∣x∣x2+23\frac{\left|{x}\right|}{x^{2} + 23} 
|x|/(x^2 + 23)
Primera derivada [src] 
sign(x)    2*x*|x|  
------- - ----------
 2                 2
x  + 23   / 2     \ 
          \x  + 23/
−2x∣x∣(x2+23)2+sign⁡(x)x2+23- \frac{2 x \left|{x}\right|}{\left(x^{2} + 23\right)^{2}} + \frac{\operatorname{sign}{\left(x \right)}}{x^{2} + 23}
Simplificar
Segunda derivada [src] 
  //          2 \                                  \
  ||       4*x  |                                  |
  ||-1 + -------|*|x|                              |
  ||           2|                                  |
  |\     23 + x /       2*x*sign(x)                |
2*|------------------ - ----------- + DiracDelta(x)|
  |           2                 2                  |
  \     23 + x            23 + x                   /
----------------------------------------------------
                            2                       
                      23 + x
2(−2xsign⁡(x)x2+23+δ(x)+(4x2x2+23−1)∣x∣x2+23)x2+23\frac{2 \left(- \frac{2 x \operatorname{sign}{\left(x \right)}}{x^{2} + 23} + \delta\left(x\right) + \frac{\left(\frac{4 x^{2}}{x^{2} + 23} - 1\right) \left|{x}\right|}{x^{2} + 23}\right)}{x^{2} + 23}
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Tercera derivada [src] 
  /                        /          2 \                /          2 \                       \
  |                        |       4*x  |                |       2*x  |                       |
  |                      3*|-1 + -------|*sign(x)   12*x*|-1 + -------|*|x|                   |
  |                        |           2|                |           2|                       |
  |  6*x*DiracDelta(x)     \     23 + x /                \     23 + x /                       |
2*|- ----------------- + ------------------------ - ----------------------- + DiracDelta(x, 1)|
  |             2                      2                            2                         |
  |       23 + x                 23 + x                    /      2\                          |
  \                                                        \23 + x /                          /
-----------------------------------------------------------------------------------------------
                                                  2                                            
                                            23 + x
2(−6xδ(x)x2+23−12x(2x2x2+23−1)∣x∣(x2+23)2+δ(1)(x)+3(4x2x2+23−1)sign⁡(x)x2+23)x2+23\frac{2 \left(- \frac{6 x \delta\left(x\right)}{x^{2} + 23} - \frac{12 x \left(\frac{2 x^{2}}{x^{2} + 23} - 1\right) \left|{x}\right|}{\left(x^{2} + 23\right)^{2}} + \delta^{\left( 1 \right)}\left( x \right) + \frac{3 \left(\frac{4 x^{2}}{x^{2} + 23} - 1\right) \operatorname{sign}{\left(x \right)}}{x^{2} + 23}\right)}{x^{2} + 23}
Simplificar
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