It is first shown that quasidifferentiable functions form a very distinct class of nondifferentiable functions. It is demonstrated that we do not need to consider any other class of nonsmooth functions, at least from the point of view of first-order approximation. The heart of quasidifferential calculus is the concept of a quasidifferential - this replaces the concept of a gradient in the smooth case and that of a subdifferential in the convex case.