Evaluating partial derivatives of two-variables functions by using maple

This article uses Maple for the auxiliary tool to study the partial differential problem of two types of two-variables functions. We can obtain the infinite series forms of any order partial derivatives of these functions by using differentiation term by term. Our research way is to count the answers by hand, and then use Maple to verify our results. This research way can not only let us find the calculation errors but also help us to revise the original thinking direction because we can verify the correctness of our theory from the consistency of hand count and Maple calculations.