Using the time-dependent Hartree-Fock method two analytical schemes are elaborated for determining the derivatives of frequency-dependent polarizability with respect to atomic Cartesian coordinates. The first scheme is iterative and consists in determining the mixed derivatives of the density matrix with respect to atomic Cartesian coordinates and dynamic electrical fields. The second takes advantage of the 2n + 1 rule to express the polarizability derivatives in terms of first-order derivatives. Both schemes are implemented in the GAMESS program. They enable the fully analytical evaluation of the Raman intensities with inclusion of the frequency dispersion. The potential of these methods is illustrated by determining the polarizability derivatives and Raman intensities of small molecules.