对数求导法的注解

The Illustration of Deriving by Taking Logarithm

主要研究利用对数求导法求导时存在的两个问题.问题1:当我们利用对数求导法时,是否不需要考虑函数的正负而直接在函数两边取对数?问题2:如果函数y有等于0的点,如何利用对数求导法求导数?另外,本文还证明了分段函数在分段点的左右导数和导数左右极限之间的关系,为求分段函数在分段点的导数提供了一种简单的方法.

This paper mainly discusses the two existing problems when deriving by taking logarithm. 1. whether directly adopting logarithm on both sides without regarding the positive or negative of the function ;2. how to derive by taking logarithm when the functions have zero factors. Otherwise, this paper also proves the relationship between the left （right） derivative and the left （right） limit of the derivative function on the piecewise point, and provides one simple method to obtain derivation on the piecewise point of the piecewise function.