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The design of an ideal differentiator is a difficult and a challenging task. In this paper, we propose two types of differentiators to estimate the time-derivative of an output signal. To begin with, a velocity estimator is proposed based on the adaptive identification method and compared with the VSS observer. Then, an acceleration estimator is proposed with the non-passifiable adaptive schemes. Finally, the proposed differentiators are applied to the estimation of the speed and acceleration of the electric throttle system modeled by Umerujan et al. The simulation results show that the proposed differentiators are robust to additive noises.