基于问题驱动的方向导数性质探讨

Research about Directional Derivative Properties Based on Problem Driven

方向导数是多元函数微分学中一个重要概念,首先给出方向导数定义,接着以问题驱动方式对方向导数性质进行剖析和探讨,深入分析方向导数与偏导数、可微、梯度、沿给定方向单调性等有关概念之间的关系。

Directional derivative is one of the most important concepts in differential calculus of pluralis-tic functions. In this paper, the concept of directional derivative is introduced, explained and deeplyanalyzed by problem-oriented approach. The relationship between the directional derivative, the par-tial derivative, differentiable functions, and monotonicity are also studied by examples.