关于对数求导法问题的探讨

A Probe into Deriving Through Logarithm

针对利用对数求导法存在的两个问题。一、是否不考虑函数的正负直接两边取对数;二、在对数式化简过程中,函数是否保持不变,利用分段函数和复合函数的求导法推出[lnf(x)]′=[ln｜f(x)｜]′=1f(x)f′(x)从而从理论上解决了对数求导法的这两个问题。

As for the two existing problems when deriving through logarithm: 1.whether directly adopting logarithm on both sides without regarding the positive or negative of the functions; 2.whether the functions keep unchangeable during the course of simplifying of the logarithm formulas. This thesis deduces［lnf(x)］'=［ln｜f(x)｜］'=1f(x)f'(x) through the deriving principles of divided-function and compound-function. Thus ,the two problems mentioned above are settled theoretically.