On additive functions which differentiate
elementary functions in some sense

Abstract. In this note, we prove that an additive function which differentiates any of a function from a rather rich list of so-called elementary functions, in some sense, is real derivation. Furthermore, we discuss the partially exceptional case of power functions and open problems will also be formulated.

Key words and phrases. Additive functions, real derivations, algebraic numbers, transcendental numbers, Gelfond–Schneider theorem.