复合函数的求导法则的合理证明及典型应用

On the Reasonable Proof and Typical Applications of the Derivation Rules of Compound Functions

高等数学中复合函数求导法则的教学一直是重、难点,高职院校的学生数学基础知识相对较差,这就给复合函数求导法则的教学带来了一定的困难。教材中对于复合函数求导法则的讲解多较为随意,并未对论证的过程进行科学合理的安排,若单纯从导数定义开展教学,很难收到良好的效果,也无法激发出学生的学习兴趣。本文主要以微分的概念为出发点,分析复合函数的求导法则的合理证明与典型应用。

The teaching of the derivation rules of compound func- tions in higher mathematics is always a key but difficult point, and the weak mathematics basic knowledge of higher vocational college students makes it more difficult. The explanations of the derivation rules of compound functions in the textbook are often cursory without scientific and reasonable proofs, but favorable ef- fects cannot be achieved and students＇ learning interest cannot be stimulated only in the teaching of the definition of derivative. Starting from the definition of differential, the reasonable proof and typical applications of the derivation rules of compound functions are mainly analyzed in this paper.