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To estimate the derivatives of a deterministic signal arriving in real time, a state observer is introduced, built as a replica of the virtual canonical model with an unknown bounded input. The results of a comparative analysis of observers with linear and piecewise linear corrective actions are presented, which are confirmed by the results of numerical modeling for piecewise differentiable composite function. Its derivatives have jump discontinuity points at the moments when the form of the function changes. It is shown that at these moments the observer variables with linear corrective actions with high gains have large surges, which increase by an order of magnitude with an increase in the order of the estimated derivative. Observers with bounded piecewise linear corrective actions do not have these problems and are recommended for use in practical applications.