Let 7Z := F [x; a, (5] be a multivariate skew polynomial ring over a division ring F. In this paper, we introduce the notion of right and left (a, (5) -partial derivatives of polynomials in 7Z and we prove some of their main properties. As an application of these results, we solve in 7Z a Hermite-type multivariate skew polynomial interpolation problem. The main technical tools and results used here are of constructive type, showing methods and algorithms to construct a polynomial in 7Z which satisfies the above Hermite-type interpolation problem and its relative Lagrange -type version. (c) 2024 Elsevier B.V. All rights reserved.