Sr Examen

Derivada de y(x)=xtg|x|

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

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Solución

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