A technique for computing the time rate of change of electron density for stratified ionospheres has been developed. The input is an initial estimate of the electron density profile and the Doppler shift at a number of frequencies in the HF band. The Doppler shift is expressed as a linear functional of the rate of change of electron density. Two techniques for inverting this linear functional to obtain the rate of change profile have been developed. Both techniques determine the values of a parametric representation of the rate of change profile that minimize the mean square error between observed and predicted Doppler shifts. One technique employs the Simplex search scheme and the second uses the method of overdetermined linear systems. It is shown that the methods converge using two test cases. A rate of change profile has been deduced from data produced by a broadband HF channel probe. There are two peaks of the profile curve in the E and F layers that occur near the two heights where the electron production rate is believed to peak. A local minimum near the peak in the F layer can be related to the formation of the F1 ledge. Applications of the rate of change profile to the study of ionospheric dynamics are discussed.