Let X be a real separable Banach algebra and K be a compact subset of X. Denote by C(K) the Banach space of continuous functions from K into X together with the uniform norm topology. We prove in this note that the operator of Gateaux derivative Dh : X → X in direction h ≠ 0 has a cyclic element f0. In other words the forward orbit Ohn(f0):={Dhn(f0)|n=1,2,⋯} is a dense subset of C(K). Also some other different cases are discussed.