Sr Examen

Derivada de xln^2abs(x)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src]
     2       
x*log (x)*|x|
xlog(x)2xx \log{\left(x \right)}^{2} \left|{x}\right|
(x*log(x)^2)*|x|
Gráfica
02468-8-6-4-2-1010-5001000
Primera derivada [src]
/   2              \            2           
\log (x) + 2*log(x)/*|x| + x*log (x)*sign(x)
xlog(x)2sign(x)+(log(x)2+2log(x))xx \log{\left(x \right)}^{2} \operatorname{sign}{\left(x \right)} + \left(\log{\left(x \right)}^{2} + 2 \log{\left(x \right)}\right) \left|{x}\right|
Segunda derivada [src]
  /     2                    (1 + log(x))*|x|                              \
2*|x*log (x)*DiracDelta(x) + ---------------- + (2 + log(x))*log(x)*sign(x)|
  \                                 x                                      /
2(xlog(x)2δ(x)+(log(x)+2)log(x)sign(x)+(log(x)+1)xx)2 \left(x \log{\left(x \right)}^{2} \delta\left(x\right) + \left(\log{\left(x \right)} + 2\right) \log{\left(x \right)} \operatorname{sign}{\left(x \right)} + \frac{\left(\log{\left(x \right)} + 1\right) \left|{x}\right|}{x}\right)
Tercera derivada [src]
  /     2                       |x|*log(x)   3*(1 + log(x))*sign(x)                                      \
2*|x*log (x)*DiracDelta(x, 1) - ---------- + ---------------------- + 3*(2 + log(x))*DiracDelta(x)*log(x)|
  |                                  2                 x                                                 |
  \                                 x                                                                    /
2(xlog(x)2δ(1)(x)+3(log(x)+2)log(x)δ(x)+3(log(x)+1)sign(x)xlog(x)xx2)2 \left(x \log{\left(x \right)}^{2} \delta^{\left( 1 \right)}\left( x \right) + 3 \left(\log{\left(x \right)} + 2\right) \log{\left(x \right)} \delta\left(x\right) + \frac{3 \left(\log{\left(x \right)} + 1\right) \operatorname{sign}{\left(x \right)}}{x} - \frac{\log{\left(x \right)} \left|{x}\right|}{x^{2}}\right)
Gráfico
Derivada de xln^2abs(x)