This paper reviews the derivative method and explores its capacity for estimating time-varying sinusoids of complicated parameter variations. The method is reformulated on a generalized signal model. We show that under certain arrangements the estimation task becomes solving a linear system, whose coefficients can be computed from discrete samples using an integration-by-parts technique. Previous derivative and reassignment methods are shown to be special cases of this generic method. We include a discussion on the continuity criterion of window design for the derivative method. The effectiveness of the method and the window design criterion are confirmed by test results. We also show that, thanks to the generalization, off-model sinusoids can be approximated by the derivative method with a sufficiently flexible model setting.