The main aim of this note is to provide characterization theorems concerning real derivations. Among others the following implication will be verified: Assume that $\xi\colon \mathbb{ R}\to \mathbb{ R}$ is a given differentiable function and for the additive function $d\colon \mathbb{ R}\to \mathbb{ R}$, the mapping \[ x\longmapsto d(\xi(x))-\xi'(x)d(x) \] is regular (e. g. measurable, continuous, locally bounded). Then $d$ is a sum of a derivation and a linear function.
Categories: math.CA