The derivative estimation problem is addressed in this paper by using Volterra integral operators which allow to obtain the estimates of the time-derivatives with fast convergence rate. A deadbeat state observer is used to provide the estimates of the derivatives with a given fixed-time convergence. The estimation bias caused by modeling error is characterized herein as well as the ISS property of the estimation error with respect to the measurement perturbation. A number of numerical examples are carried out to show the effectiveness of the proposed differentiator also including comparisons with some existing methods.