The rate of change of a function in a given direction; more precisely, if f maps an n-dimensional euclidean space into the real numbers, and x = (x₁, ..., x_n ) is a vector in this space, and u = (u₁, ..., u_n ) is a unit vector in the space (that is, u₁² +. . .+ u_n² = 1), then the directional derivative of f at x in the direction of u is the limit as h approaches zero of [f (x + hu ) - f (x)]/h.