The Gaussian regularization sampling in the linear canonical transform (LCT) domain, introduced by Annaby et al. (Signal Process. 198, 108569 2022), was developed to approximate entire functions under specific growth conditions. In this paper, we extend this technique to approximate derivatives of any order for two distinct classes of holomorphic functions, using only a finite number of samples from the original function. A rigorous error analysis is performed, providing sharp estimates based on complex analytic methods. This approach offers an exponential convergence rate and significantly improves accuracy compared to the classical LCT derivative sampling expansion. Several computational examples are presented to demonstrate the precision of the results.
