A derivative version of the well-known direct inversion in the iterative subspace (DHS) algorithm is presented. The method is used to solve the coupled perturbed Hartree-Fock (CPHF) equation to obtain the first and second derivatives of the density matrix with respect to an external electric field which, in this case, leads to the electric molecular polarizability and hyperpolarizability. Some comparisons are presented and the method shows good convergences in almost all cases. (C) 2003 Elsevier Science B.V. All rights reserved.