分段函数各段导数与分段点处导数的关系

Relationship between Derivatives of Each Section and Point of Demarcation about Piecewise Function

在分段函数求导数的学习中,学生经常不能理解在分段点处用导数定义求导,而直接对各段函数求导。从学生解题中常见的错误解法入手,引导学生提出问题。通过一些例子,讨论分段函数各段导数与分段点处导数的关系。

It is not easy to understand for many students that the definition of derivation is often applied to solve the derivative of a piecewise function at the point of demarcation. In many cases, the derivatives of each section about piecewise function are given. However, the derivative of the point of demarcation is forgotten. Based on some error solutions, students are instructed to pose problems. Through some examples, the relationship between the derivatives of each section and the point of demarcation about piecewise function is discussed.