树形图及其拓展在多元抽象复合函数求导中的应用

Application of Tree Diagram and its Expansion in Derivative of an Abstract Compound Function of Multiple Variables

多元复合函数的导数是高等数学中的重点内容,抽象复合函数的二阶导数则是其中的难点。本研究使用树形图及其拓展应用,探究多元复合函数简化且有效的求导方法。结果表明,引入拓展的树形图,可以使求多元抽象复合函数的导数变得容易理解和计算,进而极大地提高了学生的学习效率。

Derivative of multiple variables is the important content of advanced mathematics,and second derivative of an abstract compound function is its difficult point.The research uses the tree diagram and its expansion,explores the multiple compound function simplification and the effective derivation method.The results show that the introduction of tree diagram can make abstract compound function of multiple variables easier to understand and calculate,to greatly improve students’study efficiency.