Theorem on the differentiation of a composite function with a vector argument

Abstract

The paper provides a theorem on the differentiation of a composite function with a vector argument. The theorem shows how the partial derivative of the total derivative of the composite function can be expressed through the total derivative of the partial derivative of the composite function. The proof of the theorem is based on Mishkov's formula, which is the generalization of the well-known Faà di Bruno's formula for a composite function with a vector argument.