We make a comment on the recent work Boustany (2024), by showing that the Murat-Trombetti (2003) Theorem is a simple and efficient mathematical framework for nonsmooth automatic differentiation of maxpooling functions. In particular it gives a the chain rule formula which correctly defines the composition of Lipschitz-continuous functions which are piecewise C 1 . The formalism is applied to four basic examples, with some tests in PyTorch. A self contained proof of an important Stampacchia formula is in the appendix.