二元函数可微性的一个充要条件

A Necessary and Sufficient Condition for the Differentiability of Dual Function

多元函数的可微性问题教科书只给出可微的充分条件,即偏导数连续.文章把可微蕴含了各个方向的方向导数存在这一可微性的必要条件加强为充分必要条件.

As for the problem of the differentiability for dual function,a well known sufficient condition is that the partial deriuatives exist and continuous, the differentiablity implies the existion of directional derivatives,which is emphasized by the artide from being the necessary condition to a necessary and sufficient condition.