多元函数微分学是高等数学教学中的重难点,本文讨论多元函数连续、偏导、可微之间的关系。多元函数微分学是高等数学教学中的重难点,多元函数连续、偏导、可微等概念是多元函数微分学的重要概念,全面、准确地把握多元函数连续、偏导、可微等概念及其关系是学好多元函数微分学的关键。而在学习过程中,学生对多元函数连续、偏导、可微等概念及其关系往往认识的不透彻,把握的模棱两可。一、函数可微偏导存在由定理(可微的必要条件)立即可得,即若二元函数f在其定义域内一点0 0(x,y)处可微,则f在该点关 Multi-function differential calculus is a heavy difficulty in advanced mathematics teaching. This article discusses the relationship between continuous, partial derivative and differentiable functions of multiple functions. Multi-function differential calculus is a difficult and difficult point in higher mathematics teaching. The concept of continuous, partial derivative and differentiable multivariate functions is an important concept in differential function calculus. The concept of continuous, partial derivative and differentiable functions of multiple functions Their relationship is the key to learning how to differentiate multivariate functions. In the process of learning, students are ambiguous about grasping the concepts of continuous, partial derivative, differentiable functions of multiple functions and their relations. First, the existence of function deflexible partial derivatives is immediately available by the theorem (the necessary condition of differentiability), that is, if the binary function f is differentiable at a point 0 0 (x, y) in its domain, then f is at this point