A non-asymptotic algebraic procedure for the approximate, piecewise local, estimation of a finite number of time derivatives of a general time signal that may be corrupted by measurement noise is presented in this chapter. The method is based on results from differential algebra and furnishes some general formulae for the time derivatives of any measurable signal. This results are applied to the output feedback control of uncertain nonlinear systems on the basis of local time polynomial approximation of the output of the system. The case of differentially flat systems is particularly exemplified and treated in detail.