多元函数微分学是数学分析中的一个重要内容，其中有关多元函数的连续性，偏

The differential calculus of multivariate functions is an important content in mathematical analysis. Among them, the continuity of multivariate functions and the relationship between the existence of partial derivatives and differentiability are the key and difficult points of learning. Therefore, the continuity of multivariate functions can be grasped in learning. The relationship between derivative and differentiable is particularly important. In a univariate function, differentiable and derivable are equivalent. The derivation must be continuous, but the continuity is not necessarily derivable. But in multivariate functions, this relationship is not completely established. It is necessary to rethink the relationship between the continuity of multivariate functions, the existence of partial derivatives and the differentiability. <BR>This article takes a binary function as an example to specifically analyze the continuity of the binary function, the existence of partial derivatives and the difference between The relationship can be known through analysis: the function is differentiable at a certain point, then there is continuous and partial derivative at that point; the partial derivative of the function exists and continuous, then the function is differentiable. Grasp the relationship between the continuous and differentiable partial derivative of a binary function It plays an important role in understanding and mastering the related theories of subsequent multivariate functions.

Multi-function microscopy is an important content in mathematical analysis, which is related to the continuity of multi-function, the relationship between partial conductor existence and traceability is the focus and difficulty of learning, therefore, it is particularly important to grasp the continuity of multiple functions in learning, the relationship between guideable and micro-micro. In the unit function, it can be guided and slightly equivalent, it can be guided to a certain continuity, but it is not necessarily conductable. However, in multi-function, this relationship is not fully established, and it is necessary to rethink the relationship between the continuity of multiple functions, the existence of partial conductors, and the negotability.<BR>Taking the binary function as an example, this paper analyzes the relationship between the continuity of the binary function, the existence of the partial conductor and the traceability, and through the analysis, we can know that the function can be traced at a certain point, then the function is continuous at that point and there is a partial guide; Mastering the relationship between binary function bias continuity and microscopy is of great ability to understand and master the relevant theories of subsequent multiple functions.

Differential calculus of multivariate function is an important content in mathematical analysis, in which the relationship between the continuity of multivariate function, the existence of partial derivative and differentiability is the focus and difficulty of learning. Therefore, it is particularly important to grasp the relationship between the continuity and differentiability of multivariate function in learning. In univariate function, differentiability and differentiability are equivalent, differentiability must be continuous, but not continuous It is necessary to rethink the relationship among continuity, existence of partial derivatives and differentiability of multivariate functions<BR>In this paper, binary function is taken as an example to analyze the relationship between the continuity, existence and differentiability of binary function. Through the analysis, we can know that: if the function is differentiable at a certain point, it is continuous and has partial derivative at that point; if the partial derivative is continuous and has partial derivative, it is differentiable. Mastering the relationship between the continuity and differentiability of binary function's partial derivative is very important for understanding and mastering the following multivariate functions The theory of function plays an important role<BR>