The functional derivative is a generalization of the usual derivative that arises in the calculus of variations. In a functional derivative, instead of differentiating a function with respect to a variable, one differentiates a functional with respect to a function. The definition for the univariate case is (δ F[f(x)])/(δ f(y)) = lim_(ϵ->0) (F[f(x) + ϵδ(x - y)] - F[f(x)])/ϵ. For example, the Euler-Lagrange differential equation is the result of functional differentiation of the Hamiltonian action (functional).

calculus of variations | derivative | Euler-Lagrange derivative | Euler-Lagrange differential equation | functional | variation