Differentiation of Scalar and Tensor Functions of Tensor Argument

Abstract

In this paper, we analyze the existing rules for constructing derivatives of the scalar and tensor functions of the tensor argument with respect to the tensor argument and the theoretical positions underlying the construction of these rules. We perform a comparative analysis of these rules and the results obtained in the framework of these rules. Considering the existing approaches, we pay due attention to the earliest of them which for some reason is not reflected in later publications on the issue under consideration, and we give to this approach the further development.We discuss the rules for differentiation of tensor functions of the tensor argument and derivatives obtained in the publications of other authors and examine them for compliance with the construction rules and derivatives obtained in this article.