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Derivada de la función/ abs(x)/ xln(abs(x))^2

Derivada de xln(abs(x))^2

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

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Solución

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