In this paper, a design of first-order wideband digital differentiator based upon the fractional bilinear transform is presented. The Proposed design manifests the optimization of fractional bilinear transform up to 0:5π, then the bandwidth of proposed differentiator is extended by using the concept of multirate technique to cover the entire Nyquist range. It matches the ideal magnitude response perfectly with mean relative magnitude error (MRME) as low as −46:5580 (dB). The proposed first-order differentiator is compared with recently proposed differentiator designs and found to be the most accurate in terms of absolute relative magnitude error (ARME) for the entire Nyquist range.