Characterizing the derivative and the entropy function by the Leibniz rule (Q549658)

The authors study operators \(T : C^1({\mathbb R}) \to C({\mathbb R})\) satisfying the functional equation \(T(f \cdot g) = (T f) \cdot g + f \cdot (T g)\) for all \(f,g \in C^1({\mathbb R})\). They parametrize all solution operators with this property, and they also study solutions with smaller and larger domains, investigating connections with the classical derivative and entropy operators.