Faà

Faà is an Italian surname, most commonly encountered as the first part of the compound surname Faà di Bruno. The name is associated with northern Italy and is best known in modern times through the mathematician Francesco Faà di Bruno, a 19th‑century Italian mathematician and priest who authored a landmark result in calculus.

The term Faà is primarily recognized today because of Faà di Bruno's formula, the generalization of the chain rule for higher derivatives. The formula provides an explicit expression for the nth derivative of a composite function in terms of the derivatives of the outer and inner functions, with coefficients that can be described using Bell polynomials. It has applications across analysis, combinatorics, and probability theory, and appears in various mathematical texts and computational algorithms.

In broader usage, Faà as a stand-alone component of a surname is relatively uncommon outside references to the Faà di Bruno lineage. The name is primarily encountered in historical discussions of the Faà di Bruno family and in mathematical contexts related to the formula named after Francesco Faà di Bruno.