首先针对函数在区间端点的单侧导数给出反函数相应单侧导数的求导公式; 然后将反函数求导定理中的可导性条件“函数在某点可导且导数非零”分别换为“函数在某点可导且导数为0”与“函数在某点有无穷导数”, 得到反函数求导定理的各种变体.
Firstly, the unilateral derivative formulas are derived for the inverse function in terms of the unilateral derivative of a strictly monotone and continuous function. Then, some variants of the inverse function derivative theorem are obtained by respectively replacing the condition that “the derivative of the function at some point exists and is nonzero” in the original theorem with “the derivative of the function at some point is 0” and “the derivative of the function at some point is infinity”.
曾 小 林.反函数求导定理的变体[J].重庆工商大学学报（自然科学版）,2015,32(7):52-55
ZENG Xiaolin. Variants of the Inverse Function’s Derivative Theorem[J]. Journal of Chongqing Technology and Business University(Natural Science Edition）,2015,32(7):52-55