摘要:导数是世界数学史上的一座里程碑，很多国内外著名数学家在导数研究上取得了丰富的成果！九章算术中对导数的思想也有提及！目前，中学教材中增加了导数的知识，而导数的增加，给中学数学带来了新的活力。导数逐步成为研究初等函数的一个强大的工具，拓宽了数学解题的思路与方法，它不但为解决函数的极值、最值、单调性的问题提供了简便方法，而且在不等式证明，恒等式证明以及数列求和方面有着广泛的应用，这样加深了学生对于函数问题的理解，培养了学生分析问题解决问题的能力，并丰富了解题方法的多样性！通过对导数解决初等数学方面的研究，归纳总结导数在解题中的用法和技巧，以及各方面的灵活应用，让导数立体般的呈现在大家眼前，更好的体现高等数学在解决初等数学问题当中的实用性。

关键词:导数 函数 不等式 恒等式 数列求和

Abstracts:The derivative of a milestone in the history of mathematics in the world, many famous domestic and foreign mathematicians in the study of the derivative has achieved fruitful results! Nine Chapters on the Mathematical of derivative ideas mentioned. Secondary school textbooks to increase the knowledge of the derivative, the derivative of the increase brought new vitality to the middle school mathematics. Derivative gradually become a powerful tool to study elementary functions, expand the scope of the ideas and methods of mathematical problem solving, it is not only to solve the extreme value of the function, the most value, monotonicity provides a convenient way, and the inequality to prove the identities proved series summation has a wide range of applications, so that deepen students' understanding of the function problem, and train students to analyze and solve problems, and enrich the diversity of problem-solving methods. Derivative in elementary mathematics, inductive summary of derivative in solving problems usage and skills, as well as various aspects of flexible applications, derivative three-dimensional like the in front of everyone, to better reflect the higher mathematics in the solve elementary mathematical problem among the practicality.

Keywords：Derivative Function Inequality Identity  Several Summation

在高等数学中,导数及导数的应用是一个重要的内容，它处于一个特殊的地位，是与中学知识的一个重要交汇点，是联系很多相关数学知识以及解决有关问题的重要工具。用导数解决初等数学问题，可以降低计算难度，淡化计算技巧，从而拓展学生的解题空间，提高学生的解题能力。因此，归纳总结导数在解初等函数问题中的用法，技能以及灵活运用，使导数立体般呈现在大家眼前，可以更好的体现出高等数学在解决初等数学问题中的实用性。下面谈一谈对导数的具体认识。