关于指数函数导数教学的新设计  

The New Teaching Design of derivative of the Exponential Function

作　　者：王敏[1] 

机构地区：[1]绵阳师范学院数理学院,四川绵阳621000

出　　处：《绵阳师范学院学报》2016年第11期9-12,共4页Journal of Mianyang Teachers＇ College

摘　　要：本文阐述了在教学实践中关于指数函数与对数函数导数教学中的新设计,旨在帮助学生深刻理解导数公式推导过程与重要极限“lim_（x→∞）（1＋1/x）-x=e.”的关系,直观地给出自然指数函数和自然对数函数的底“e”的存在性说明,同时绕开晦涩难于理解的极限存在准则,利用导数思想证明了重要极限“lim_（x→∞）（1＋1/x）-x=e.”给出了“e”的另一种定义方式,丰富了高等数学教学中的教学手段.This paper elaborates the new teaching design of derivative of the exponential function, aiming to help students understand comprehensively the relation between the derivative formula derivation and the significant ＂lim_（x→∞）（1＋1/x）-x=e.＂ We intuitively show the existence of the base ＂ e＂ of the natural exponential function and natural logarithm function and give the proof of the significant limit formula ＂lim_（x→∞）（1＋1/x）-x=e.＂ Meanwhile, existence of we use the idea of derivative to limit. This design enriches the give another way of expression of ＂e＂ bypassing the elusive rule of the methods of teaching advanced mathematics.

关 键 词：指数函数 对数函数 limx→∞（1＋1/x）^x=e. 导数 

分 类 号：O172.1[理学—数学]