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