浅谈导数在研究数学问题中的若干应用

The Application of Derivatives in the Study of Mathematical Problems

导数和微分是数学分析中的一个重要分支,有了导数这个重要工具,数学中很多复杂的问题变得简单,甚至一些疑难问题也迎刃而解。本文意在探讨导数在证明恒等式、求极限、讨论函数的单调性、极值等方面的应用,感受导数美、数学美。

Derivative and differential are an important branch in mathematical analysis.As derivative is an important tool,many complex problems in mathematics become simple and even some difficult problems can be solved easily.The purpose of this paper is to explore the application of derivative in proving identities,finding limit,discussing monotonicity and extreme value of function,and to feel the beauty of derivative and mathematics.