This paper takes the mathematical software Maple as the auxiliary tool to study the differential problems of four types of functions. We can obtain the infinite series forms of any order derivatives of these functions by using binomial theorem and differentiation term by term theorem, and hence greatly reduce the difficulty of calculating their higher order derivative values. On the other hand, we propose two examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple.

derivatives, infinite series forms, binomial theorem, differentiation term by term theorem, Maple