人们做事总想“快”又“巧”,事半功倍。数学形式千变万化,方法繁多。在解题时如何灵活地运用知识,使解题既快又巧,这不仅有利于加深对基础知识的理解,更重要的是学到灵活解题的思想与方法。因此,数学教学中,“巧”字不容忽视。下面结合《导数与微分》的数学,谈谈自己的一些体会。一、要“巧”,首先概念要清,要清晰地把握住数学规律的本质。导数和微分是微积分中的基本概念,求初等函数的导数是该章的重点,是学习微积分必备的基本技能。要求导,就必须利用基本初等函数的求导公式及法则,而每个公式及法则都是直接或间接根据导数 People always want to be “fast” and “smart” and do more with less. The form of mathematics is ever-changing, with many methods. How to apply knowledge flexibly when solving a problem, so that solving problems is fast and skillful, which not only helps deepen the understanding of basic knowledge, more importantly, it learns the ideas and methods of solving problems flexibly. Therefore, in mathematics teaching, the word “skillful” cannot be ignored. In the following, we will discuss some of our experiences with the mathematics of Derivatives and Differentials. First, we must “cleverly”. First of all, the concept must be clear. We must clearly grasp the nature of the mathematical law. Derivatives and differentials are basic concepts in calculus. Finding derivatives of elementary functions is the focus of this chapter and is a basic skill for learning calculus. Asked to guide, we must use the basic derivative function of the derivative formula and law, and each formula and rule are directly or indirectly based on the derivative