|x| x*sign(x)
--- + ---------
2 2
$$\frac{x \operatorname{sign}{\left(x \right)}}{2} + \frac{\left|{x}\right|}{2}$$
x*DiracDelta(x) + sign(x)
$$x \delta\left(x\right) + \operatorname{sign}{\left(x \right)}$$
3*DiracDelta(x) + x*DiracDelta(x, 1)
$$x \delta^{\left( 1 \right)}\left( x \right) + 3 \delta\left(x\right)$$