A derivation is a sequence of steps, logical or computational, from one result to another. The word derivation comes from the word "derive."

"Derivation" can also refer to a particular type of operator used to define a derivation algebra on a ring or algebra.
In particular, let
be a Banach algebra and be a Banach -bimodule. Any element of

is called a bounded derivation of in
and any element of

Helemskii, A. Ya. The Homology of Banach and Topological Algebras. Dordrecht, Netherlands: Kluwer,
1989.Helemskii, A. Ya. Banach
and Locally Convex Algebras. Oxford, England: Oxford University Press, 1993.Helemskii,
A. Ya. "The Homology in Algebra of Analysis." In Handbook of Algebra,
Vol. 2. Amsterdam, Netherlands: Elsevier, 1997.