Faà di Bruno公式在函数逐次求导上的应用

Application of Faà di Bruno in calculating the successive derivatives of function

给出了Fa dibruno公式在函数逐次求导上的应用定理并给出了证明 ,同时应用此定理给出了一些抽象复合函数的逐次导数 ,并利用Stirling数对结果进行简化。为进一步研究更加复杂的函数的导数及其性质打下了基础。

This paper presents and proves the theorem about application of the Fa bruno formula in calculating successive derivatives of some functions. At the same time, it puts forward successive derivatives of some abstract compound functions and simplifies the result by making use of Stirling Number. These are employed to build the base for studying the derivatives and the characteristics of more complicated function.