摘要
导数是微积分学的重要研究对象,寻求函数的高阶导数公式是困难的,只有极少数类型的函数可以得到高阶导数公式.本文给出了有理函数的高阶导数的公式,我们从分解真分式入手,由于任意一个真分式都可以分解成最高分式之和,再利用导数的运算法则及公式,把复数部分转换为三角式进行化简,进而推算出有理函数的高阶导数的公式.最后本文结合实例对有理函数的高阶求导做出了讨论.
Derivative is an important subject of calculus.It is difficult to find a formula for the derivative number of a function,and only a very few types of functions can get the derivative number formula.The formula of derivative number of rational function is given in this paper.We start with splitting the real fraction,since any one true fraction can be decomposed into the sum of the highest fractions,then by using the derivative′s algorithm and formula,the plural part is converted to a triangular type for simplifying,and then the formula of the derivative number of the rational function is deduced.Finally,this paper discusses the higher order derivation of rational function with examples.
作者
江君
单壮
王彦超
JIANG Jun;SHAN Zhuang;WANG Yan-chao(School of Sugon Big Data,Liaoning Institute of Science and Technology,Benxi Liaoning 117004,China)
出处
《大学数学》
2018年第5期118-122,共5页
College Mathematics
基金
辽宁省教育厅科学技术研究青年项目(L2017lkyqn-01)
辽宁科技学院青年基金(Qn201603)
关键词
有理函数
高阶导数
待定系数法
rational function
higher-order derivative
the method of undetermined coefficients
