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Derivada de la función/ abs(x)/ x*ln(abs(x))

Derivada de x*ln(abs(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] 
x*sign(x)           
--------- + log(|x|)
   |x|
$$\frac{x \operatorname{sign}{\left(x \right)}}{\left|{x}\right|} + \log{\left(\left|{x}\right| \right)}$$
Simplificar
Segunda derivada [src] 
  /      2                     \            
  |  sign (x)   2*DiracDelta(x)|   2*sign(x)
x*|- -------- + ---------------| + ---------
  |      2            |x|      |      |x|   
  \     x                      /
$$x \left(\frac{2 \delta\left(x\right)}{\left|{x}\right|} - \frac{\operatorname{sign}^{2}{\left(x \right)}}{x^{2}}\right) + \frac{2 \operatorname{sign}{\left(x \right)}}{\left|{x}\right|}$$
Simplificar
Tercera derivada [src] 
        2          /    2                                                \                  
  3*sign (x)       |sign (x)   DiracDelta(x, 1)   3*DiracDelta(x)*sign(x)|   6*DiracDelta(x)
- ---------- + 2*x*|-------- + ---------------- - -----------------------| + ---------------
       2           |    3            |x|                      2          |         |x|      
      x            \   x                                     x           /
$$2 x \left(\frac{\delta^{\left( 1 \right)}\left( x \right)}{\left|{x}\right|} - \frac{3 \delta\left(x\right) \operatorname{sign}{\left(x \right)}}{x^{2}} + \frac{\operatorname{sign}^{2}{\left(x \right)}}{x^{3}}\right) + \frac{6 \delta\left(x\right)}{\left|{x}\right|} - \frac{3 \operatorname{sign}^{2}{\left(x \right)}}{x^{2}}$$
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