In mathematics, certain functors may be derived to obtain other functors closely related to the original ones.

The technique of taking a left/right exact functor $\mathcal{F}$ between abelian categories and deriving a collection of functors $\{R^\bullet\mathcal{F}\}$ such that $R^0\mathcal{F} = \mathcal{F}$ with certain desirable compatible properties (e.g., long exact sequence). Reference: Wikipedia.

This operation, while fairly abstract, unifies a number of constructions throughout mathematics (e.g., derived functors of the $\hom$ and $\otimes$-functor between $R-\mathsf{Mod}$ are $\text{Ext}^n$ and $\text{Tor}^n$-functors of homological algebra, respectively).