A delta-function potential model is used to derive an analytical expression for the derivative of the mean molecular polarizability with respect to a change in the internuclear distance at the equilibrium configuration for symmetrical stretching modes in the ground electronic states of diatomic and polyatomic systems. The calculated polarizability derivatives are in reasonable agreement with the experimental ones derived from Raman intensities. Bond orders are calculated from experimental polarizability derivatives for various ionic systems and the results are discussed.