摘要
本文首先依托两个典型例题为载体深度剖析导数定义,并给出结论“在一点连续的前提下,双动点差商的极限存在则函数在该点可导”的一种新证明。然后利用导数定义和导数极限定理去分析和解决分段函数的导数问题,并进一步探究了导数极限定理的本质为导函数的连续性。
This paper examines the definition of the derivative through two examples and offers a new proof that,for a continuous function at a point,the existence of the double moving-point difference quo-tient limit implies differentiability.It then applies the definition and the derivative limit theorem to piece-wise functions and interprets the theorem as expressing the continuity of the derivative.
作者
宋莉莉
王继宏
SONG Lili;WANG Jihong(School of Mathematics and Physics,Southwest University of Science and Technology,Mianyang 621010)
出处
《高等数学研究》
2025年第5期67-70,F0003,共5页
Studies in College Mathematics
基金
西南科技大学教育教学改革与研究项目(22xn0029)
西南科技大学课程建设类项目(25CJAL22).
关键词
导数定义
导数极限定理
分段函数的导数
导函数的连续性
definition of derivative
derivative limit theorem
derivative of piecewise function
continuity of derivativefunction
