Four derivatives-based autofocus criteria functions are proposed through bringing several applicable computational methods of derivatives into the study of autofocus algorithms for the digital holographic imaging. By analyzing the transfer of noise produced during recording in phase shifting digital holography,the impact of noise on the derivatives-based autofocus algorithms is investigated. The results from the simulation and experiment indicate Prewitt gradient (PRG) and Tenebaum gradient (TEG) criteria functions,together with the angular spectrum reconstruction routine can form two types of efficient and reliable autofocus algorithms.