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”.