quality:correction
Antiderivative and derivative

The ramp function is an antiderivative of the Heaviside step function: ∫ − ∞ x H (ξ) d ξ = x H (x) = max { 0, x }. {\displaystyle \int _{-\infty }^{x}H(\xi)\,d\xi =xH(x)=\max\{0,x\}\,.}

The distributional derivative of the Heaviside step function is the Dirac delta function: d H (x) d x = δ (x). {\displaystyle {\frac {dH(x)}{dx}}=\delta (x)\,.}