let A be a fuzzy subset of a universe X and f a map of X to Y. Let mu_A be the membership function of A and f ^ {~} the Zadeh's extension of f. So mu_ {f ^{~} (A)} is the membership function of f ^ {~} (A) given by the Zadeh's extension. Suppose that mu_A is differentiable, So what is the condition for mu_ {f ^ {~} (A)} to be differentiable?