本文通过对导数在研究函数的单调性、极值,以及函数不等式中的应用进行分析,拓展了数学解题方法的研究领域,开辟了许多新的解题途径,加深了学生对函数及其性质的理解和直观认识。文中还提出了利用导数解数学问题可以采用创造性思维、联想思维及化归思维等几个主要的思维策略。 This paper analyzes the application of derivatives in monotonicity, extremum and function inequality of research functions, expands the research field of mathematical problem solving methods, opens up many new ways of solving problems, deepens the students’ Understanding and intuitive understanding. The article also proposed several key thinking tactics such as creative thinking, conjunctive thinking and returning to thinking.