复合函数求导法则定义域放大问题的原因探究与解决办法

Exploration and Solution to the Problem of Enlarging the Definition Domain of the Derivation Rule of Composite Functions

摘要: 复合函数求导法则是微积分学中非常重要和应用非常广泛的求导法则，是高等数学教材和高中数学教材中必学必教内容，复合函数求导法则的证明过程是没有问题的，但是在某一类一元函数求导应用中存在原函数和导函数定义域不一致的副作用，本文通过教材中实际存在的例题和构造的例题说明了，复合函数求导放大定义域这一问题，并且探讨了可能出现这一问题的原因，同时给出了严谨的复合函数使用的格式。

Abstract: Composite function derivation rule is a very important and widely used derivation rule in calculus, and is a must-learn in advanced mathematics textbooks and high school mathematics textbooks. The proof process of composite function derivation law is no problem, but in a certain class of univariate function derivation application, there are side effects of inconsistency between the original function and the derivative function definition domain. This paper through the actual examples and construction examples in the textbook to illustrate, composite function derivation amplified definition domain problem. The reasons for this problem are discussed, and the format used by rigorous composite functions is given.