This paper takes the mathematical software Maple as the auxiliary tool to study the partial differential problem of three types of multivariable functions. We can obtain the infinite series forms of any order partial derivatives of these multivariable functions by using differentiation term by term theorem, and hence greatly reduce the difficulty of calculating their higher order partial derivative values. On the other hand, we propose some 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.

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