adj. 1. (of a function or operator) possessing a well-defined derivative. See also manifold. 2. (of a function of the real variables x₁,..., x_n) having partial derivatives such that near the point (a₁,..., a_n), where ɛ tends to zero as (x₁,..., x_n) tends to (a₁,..., a_n), and f_xi is the partial derivative of f with respect to x_i.