摘要
在微积分学中,莱布尼兹给出了两个函数乘积的高阶导数的公式.但是,复合函数的高阶导数公式却鲜为人知.本文介绍了解决此问题的Faàdi Bruno公式并利用多项式定理和泰勒公式给出此公式的一种证明.最后讨论了此公式在微积分和组合数学中的一些应用.
Leibniz’s formula for the higher derivatives of a product of two functions is well known in calculus.Less known is the formula for the higher derivatives of a composition of two functions.In this paper,Faàdi Bruno Formula is introduced to solve this problem and a new proof of this formula is obtained by Taylor theorem and multinomial theorem.Lastly,we give some applications of this formula in calculus and combinatorics.
作者
李志国
邵泽玲
李志新
LI Zhi-guo;SHAO Ze-ling;LI Zhi-xin(School of Sciences, Hebei University of Technology, Tianjin 300401, China;School of Mathematics and Physics, Hebei University of Engineering, Handan Hebei 056038, China)
出处
《大学数学》
2020年第6期97-100,共4页
College Mathematics
基金
河北工业大学教育教学改革研究项目(201903028)
河北省自然科学面上基金(A2019402043)。
