本篇論文主要是研究複數冪級數在四種函數微分問題上的應用。我們利用逐項微分定理可以求出這四種函數的任意階導函數，因此大大降低了求解它們高階微分值的困難度。此外，我們舉出四個函數實際的求出它們的任意階導函數以及一些它們的高階微分值，而這些高階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計算出這些高階微分值以及它們無窮級數表示法的近似值。

This paper mainly studies the application of complex power series to the differential problems of four types of functions. We can obtain any order derivatives of these four types of functions by using differentiation term by term theorem, and hence greatly reduce the difficulty of evaluating their higher order derivative values. In addition, we propose four functions to find their any order derivatives and some of their higher order derivative values practically, and the answers of these higher order 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 derivative values and their infinite series forms.