A great number of Artificial Intelligence applications are based on features extracted from signals or images. Feature extraction often requires differentiation of discrete signals and/or images in one or more dimensions. In this work we provide two Theorems for the construction of finite length (finite impulse response -FIR) masks for signal and image differentiation of any order, using central differences of any required length. Moreover, we present a very efficient algorithm for implementing the compact (implicit) differentiation of discrete signals and images, as infinite impulse response (IIR) filters. The differentiator operators are assessed in terms of their spectral properties, as well as in terms of the performance of corner detection in gray scale images, achieving higher sensitivity than standard operators. These features are considered very important for computer vision systems. The computational complexity for the centered and the explicit derivatives is also provided.