Minerals have unique spectral signatures that can be used for their identification similar to a fingerprint. Although some minerals have extremely similar compositions thus comparable signatures, they can be differentiated through remote sensing. Therefore, a derivative spectrum was used in this study, which enhanced the subtle spectral discrepancies to help determine whether a special order of a derivative spectrum is applicable in discrimination of these mineral targets. Second, we investigated whether derivative spectra in higher orders can be applied to discriminate between mineral targets using those in five orders as an input for a similarity measure (Jeffries-Matusita distance). Results of this study have shown that the best derivative order selection for each target is a target-specific problem. The first and fourth derivative orders were the bests for alunite and quartz minerals, respectively. As spectral smoothing is a preliminary process of derivative analysis, its bandwidth influence on derivative spectra was then investigated, and a smoothing window size of five sampling points was considered. Based on the results of this study, we recommend the introduction of high-order derivative spectra as the input for many detectors or classifiers in remote sensing especially for differentiation of minerals such as phengite, muscovite, and sericite.