adj. 1. of, pertaining to, or containing derivatives. 2. (as substantive) an increment in a given function, expressed as the product of the derivative of that function and the corresponding increment of the independent variable; if F(x) is the given function, then (However, when dx is an increment in x, dF is not in general the increment in F.) 3. (as substantive) an increment in a given function of two or more variables, expressed as the sum of the products of each partial derivative and the increment in the corresponding variable; if F(x₁,..., x_n) is the given function, then (However, when dx_i are the increments in x_i, dF is not in general the increment in F.) 4. (as substantive) a mapping, df, derived from a given mapping, f, between two normed vector spaces, such that See also Frechet differential, Gateaux differential.