Science and Education Publishing International Journal of Partial Differential Equations and Applications ISSN Pending 2 1 2014 01 16 Application of Differentiation Term by Term Theorem on the Partial Differential Problems 7 12 EN Chii-Huei Yu Department of Management and Information, Nan Jeon University of Science and Technology, Tainan City, Taiwan IJPDEA2014212 10.12691/ijpdea-2-1-2 2013 11 24 2014 01 05 2014 01 16 This paper takes the mathematical software Maple as the auxiliary tool to study the partial differential problems of two types of two-variables functions. We can obtain the infinite series forms of any order partial derivatives of these two types of 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 two examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying our answers by using Maple.