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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 approximate differentiator with first order low pass filter. Then, an acceleration estimator is proposed with the non-passifiable adaptive schemes. Finally, the proposed differentiators are applied to the feedback control system of an active suspension system. The simulation results show that the proposed differentiators are robust to additive noises.