“对数求导法”合理性分析

Rationality Analysis of the Logarithmic Derivation Method

部分函数求导可利用"对数求导法"进行求解,方便快捷,但用这种方法求导时有些运算并不够严密,需要做进一步深层次分析研究才能更好地运用到实际问题中。初等函数在可导的区间内,其导函数在各个分区间内具有相同的算式结构,用"对数求导法"求初等函数导数时,只需在某个能使取对数恒等变型且有意义的情况下求解,然后将结果扩展到其他可导区间上即可。

The derivation of some functions can be solved by the logarithmic derivation method,which is convenient and quick.However,some operations are not rigorous enough when using this method to derive,and further deep analysis and research are needed to make better use of it.The derivative function of the elementary function in the derivable interval has the same formula structure among the partitions.When using the logarithmic derivation method to find the derivatives of elementary functions,one only needs to solve the equation by making the logarithmic identity variant and meaningful case,then extend the result to other derivable intervals.