对多元复合函数偏导数求解的研究

Research on Solving Partial Derivatives of Multivariate Compound Functions

摘要: 本文主要讨论多元复合函数的偏导数问题，主要对中间变量是隐函数的情况进行讨论。文章主线是从隐函数的存在性问题出发，并结合“链式求导法则、矩阵求多元抽象复合函数二阶偏导数”等技巧和方法，获得了求解多元复合函数的一、二阶偏导数的理论性定理。

Abstract: In this article, we mainly discuss the partial derivatives of multivariate compound functions, and mainly discuss the case that the intermediate variables are implicit functions. The main line of this article starts from the existence of implicit function, and combines the techniques and methods of “chain derivative rule, using matrix to find the second partial derivative of multiple abstract composite function”. The theoretical theorems for solving the first and second partial derivatives of multivariate compound functions are obtained.