兩種有理函數的微分問題

The Differential Problem of Two Types of Rational Functions

本篇論文主要是研究兩種有理函數的微分問題。我們利用Leibniz微分法則可以得到這兩種有理函數任意階導函數的閉合型式解，因此大大降低了求解它們高階微分值的困難度。此外，我們舉出兩個有理函數的例子實際的求出它們的任意階導函數的閉合型式解以及一些它們的高階微分值。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解的近似值。

This paper mainly studies the differential problem of two types of rationalfunctions. We can obtain the closed forms of any order derivatives of these two types of rational functions by using Leibniz differential rule, and hence reducing the difficulty of evaluating their higher order derivative values greatly. In addition, we propose two examples of rational functions to find the closed forms of their any order derivatives and calculate some of their higher order derivative values practically. On the other hand, we employ the mathematical software Maple to calculate the approximations of these higher order derivative values and their solutions.