关于多元复合函数高阶求导的讨论  

A New Method for Higher Order Derivative of Multivariate Composite Function

作　　者：文传军[1] 华婷[1] 

机构地区：[1]常州工学院理学院,江苏常州213002

出　　处：《常州工学院学报》2010年第4期54-56,共3页Journal of Changzhou Institute of Technology

摘　　要：多元复合函数高阶求导是高等数学教学中的难点,其计算较为复杂和繁琐。文章针对该问题进行了研究,利用矩阵和向量以整体形式表现计算的过程和结果,并借助代换计算的方式计算中间变量导函数对自变量的求导,从而得到复合函数高阶求导的简单方法。The higher order derivative calculation of multivariate composite function is a difficult point in teaching higher mathematics,and its derivation computation is complex and tedious.This paper studies the method for higher order derivative of multivariate composite function.Vector-matrix form is utilized to express derivative calculation progress and result in a whole and substitution is applied in the derivative computation of midst-variable derived function to independent variable,which leads to a new and easy approach to this question.

关 键 词：多元复合函数 高阶求导 矩阵向量形式 代换 

分 类 号：O174[理学—数学]