(untitled) (Journal of Computational Mathematics, 2021)
In this paper, we consider the higher divided difference of a composite function f(g(t)) in which g(t) is an s-dimensional vector. By exploiting some properties from mixed partial divided differences and multivariate Newton interpolation, we generalize the divided difference form of Faà di Bruno's formula with a scalar argument. Moreover, a generalized Faà di Bruno's formula with a vector argument is derived.