本篇論文主要是研究四種兩變數函數的偏微分問題。我們利用逐項微分定理和幾何級數定理可以求出這四種兩變數函數的任意階偏導函數，因此大大降低了求解這些兩變數函數高階偏微分值的困難度。此外，我們舉出四個兩變數函數的例子實際的求出它們的任意階偏導函數以及一些它們的高階偏微分值，而這些高階偏微分值的答案都是以無窮級數的型式呈現的。另一方面，我們利用數學軟體 Maple 計算出這些高階偏微分值以及它們無窮級數表示式的近似值來驗證我們的答案。

This paper mainly studies the partial differential problem of four types of two-variables functions. We can obtain any order partial derivatives of these four types of two-variables functions by using differentiation term by term theorem and geometric series theorem, and hence greatly reduce the difficulty of evaluating their higher order partial derivative values. In addition, we propose four examples of two-variables functions to find their any order partial derivatives and some of their higher order partial derivative values practically, and the answers of these higher order partial derivative values are presented in infinite series forms. On the other hand, we employ the mathematical software Maple to calculate the approximations of these higher order partial derivative values and their infinite series forms to verify our answers.