In this paper, two methods for designing digital full-band FIR differentiators are presented. First of them, named Immediate, represents the efficient and general method for brusque designing the first and higher degree digital full-band FIR differentiators of even and odd order, with simultaneous approximation of the prescribed magnitude and group delay responses, using originally modified eigenfilter method. The proposed method presents an approach for the FIR differentiator frequency response approximation directly in the complex, and not in the real domain. The second method, named Intermediary, represents the efficient approach for oblique designing only the second and higher degree digital full-band FIR differentiators of odd order. The comparison of the characteristics and results of these two presented methods is performed. In order to illustrate the presented methods effectiveness, the numerical design examples of the first second degree full-band digital differentiators are given, too.