  We explore a differential calculus on the algebra of smooth functions on a
manifold. The former is `noncommutative' in the sense that functions and
differentials do not commute, in general. Relations with bicovariant
differential calculus on certain quantum groups and stochastic calculus are
discussed. A similar differential calculus on a superspace is shown to be
related to the Batalin-Vilkovisky antifield formalism.
