# 5.2 $S_b'[x]$: First-Order Derivative of Unit-Step Staircase Function

The Fourier series for the first-order derivative $S_b'[x]$ of the staircase function evaluates to $2\ f$ at positive integers where $f$ is the evaluation frequency limit. Note in the case of $S_b'[x]$, the evaluation at an integer value of $x$ is always exactly at the peak of the primary lobe associated with the integer $x$. Note  $S'[x]$ is the Fourier series for the Dirac comb.