Gentle algebras, introduced by Assem and Skowroński, are a well-loved class of algebras. They are string algebras, so their module categories are combinatorially described in terms of strings and bands, they are tiling algebras associated with dissections of surfaces, and they have many other remarkable properties. Furthermore, Jacobian algebras arising from triangulations of unpunctured marked surfaces are gentle. In this talk, I will present a multiplication formula for cluster characters induced by generating extensions in a gentle algebra A. This formula generalizes a previous result of Cerulli Irelli, Esposito, Franzen, and Reineke. Moreover, in the case where A comes from a triangulation T, it provides a representation-theoretic interpretation of the exchange relations in the cluster algebra with principal coefficients in T.