Abstract: In Reference(1), the question of derivation of absolute value function has been solved. Its results are extended to general piecewise functions in this paper. First, two lemmas are given, and then the necessary and suffiei ent condition of piecewise functions at their dividing points and its corollary are obtained.

Key words: Dividing point of piecewise function, Derivative on the left or on the right, Derivative limit on the left or on the right