Partial stabilities and partial derivations of nn-variable functions

We introduce the concepts of the partial derivations of a function from a normed algebra A1×⋯×AnA1×⋯×An into a Banach algebra BB and prove the Hyers–Ulam–Rassias stability of the function. Moreover, we obtain some results about the applications of derivations such as the extended derivations and the approximately higher derivations.