证明不等式是初等数学乃至高等数学中最基本的内容之一,而导数是分析、证明不等式中常用的重要工具,在高中数学的解题中有着广泛的应用,本文探讨了利用导数证明不等式的几种常见方法:一次利用或多次叠用一阶导数、利用二阶导数、分段利用一阶导数、利用函数取对数求导数、变量替换求函数导数等的证明方法,突出了不等式证明的基本思想和基本方法;同时,给出了重要数列{(1+1/n)~n}的单调性和有界性的简单证明。 It is proved that the inequality is one of the basic contents of elementary mathematics and even advanced mathematics. The derivative is an important tool used to analyze and prove the inequality. It has a wide range of applications in the solution of high school mathematics. This paper discusses the use of derivatives to prove inequality. Common methods: Proof methods using one or more multiples of first derivative, second derivative, piecewise use of first derivative, use of function to take logarithm to find derivative, variable substitution to find function derivative, etc., highlight the inequality proofs Basic ideas and basic methods; At the same time, a simple proof of the monotonicity and boundedness of important sequences {(1+1/n)~n} is given.