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Derivada de la función/ (|x|)/ x-log(|x|)

Derivada de x-log(|x|)

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

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Solución

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