中学基本初等函数导数的高观点证明

A High View Proof of the Derivative of Basic Elementary Functions in Middle School

摘要: 初等数学作为高等数学层面上的特例，往往不一定对所有数学概念、命题和数学系统满足逻辑和结果的无矛盾性。本文以高等数学范畴的两个重要极限给出对指数函数、对数函数、正弦函数和余弦函数的导数的证明，提高和拓宽学生的思维视角和逻辑起点，并利用高观点的数学思想方法来审视中学教学。

Abstract: As a special case of higher mathematics, elementary mathematics often does not necessarily satisfy the contradiction-free logic and results for all mathematical concepts, propositions and mathemati-cal systems. This paper gives the proof of the derivative of exponential function, logarithmic func-tion, sine function and cosine function with two important limits of the category of higher mathe-matics, so as to improve and broaden the students’ thinking perspective and logical starting point, and use the mathematical thinking method of high point of view to examine middle school teaching.