# 5.9 $M_b'[x]$: First-Order Derivative of Third “Chebyshev-like” Function

The Fourier series for the first-order derivative $M_b'[x]$ of the third “Chebyshev-like” function evaluates to $2\ f\ n\ \log[p]$ at prime-powers of the form $x=p^n$ where $f$ is the evaluation frequency limit. The reference function in the following plots is $2\ f\ \log[Abs[x]]$.