变限积分函数求导数的F-方法  

The F-method of calculating the derivative of the variable limit integral function

作　　者：侯玉双[1] 何莉敏[1] HOU Yushuang;HE Limin(School of Science,Inner Mongolia University of Science and Technology,Baotou 014010,China)

机构地区：[1]内蒙古科技大学理学院,内蒙古包头014010

出　　处：《高师理科学刊》2020年第9期46-48,66,共4页Journal of Science of Teachers＇College and University

基　　金：内蒙古自治区自然科学基金项目(2019MS06022)。

摘　　要：针对学生在学习变限积分函数求导数时通常出现的3类错误,结合牛顿-莱布尼兹公式及一元复合函数的链式求导法则,提出变限积分函数求导数的F-方法.这种方法通过简记变限积分函数中被积函数的原函数为F,而不需求出F的具体解析表达式,以F为桥梁,先写出变限积分函数的牛顿-莱布尼兹公式,再对其运用一元复合函数的链式求导法则,求出变限积分函数的导数.通过实例表明,利用这种方法学生可以简便准确地求出变限积分函数的导数.In view of the three common mistakes of students in learning the derivative of variable limit integral function,combining Newton-Leibniz formula and chain derivative rule of one variable compound function,the F-method for derivative of variable limit integral function is proposed.In this method,the original function of the integrand in the variable limit integral function is simplified as F,instead of the specific analytical expression of F.Taking F as a bridge,the Newton Leibniz formula of the variable limit integral function is written first,and then the derivative of the variable limit integral function is obtained by using the chain derivative rule of the one variable compound function.Some examples show that students can easily and accurately calculate the derivative of the variable limit integral function by using this method.

关 键 词：变限积分函数 导数 牛顿-莱布尼兹公式 原函数 被积函数 

分 类 号：O173[理学—数学] G642.0[理学—基础数学]