Terahertz (THz) communication has emerged as one of the key technologies for sixth-generation (6G) wireless networks. Nevertheless, the transition to higher operational frequencies poses various challenges including high-speed digital-to-analog conversion (DACs) and analog-to-digital conversion (ADCs), heterogeneous integration of optoelectronic devices, resulting in an urgent need for solutions. In this paper, we demonstrate a groundbreaking THz analog differential operator driven by diffractive neural networks (DNN), implementing ultra-fast and high-throughput analog domain differential operations. The designed multilayer all-optical DNN composed of compact dielectric metasurfaces is trained with trigonometric functions to perform analog differential computing of complex input signals by approximating the differentiation of finite decompositions of time-domain function based on the Fourier transform theory, significantly improving integration, throughput, and processing speed. Our design has been experimentally validated to successfully implement single-direction differential operation on one- and two-dimensional signals with superior structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR), providing a promising path for the development of integrated and ultrafast THz communication systems.