We show that polynomial hitting set generator defined by Shpilka and Volkovich [1] has the following property: If an n-variate polynomial f has a partition of variables such that the partial derivative matrix [2] has large rank then its image under the Shpilka-Volkovich generator too has large rank of the partial derivative matrix even under a random partition. Further, we observe that our main result is applicable to a larger class of hitting set generators that are defined by polynomials that can be represented as a small sum of products of univariate polynomials. © 2019 Elsevier B.V.