This paper discusses the estimation of non-stationary sinusoidal parameters. We formulate a piecewise version of the distributive derivative algorithm, which is used to analyse non-stationary sinusoidal signals and estimate their frequencies and log amplitude derivatives over a long duration as spline functions, and apply this algorithm for the estimation of instantaneous frequencies, amplitudes and phase angles. Test results show that the piecewise derivative algorithm provides better estimation than the previous non-piecewise version at lower computation cost.