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Spectral mixture analysis (SMA) has been used extensively in the hyperspectral remote sensing community for the subpixel abundance estimation of targets. However, the task of defining every endmember can be difficult, as evident from the importance attributed to the topic in the recent literature. The effectiveness of SMA can be compromised when the required spectral endmembers are not well constrained in terms of their spectral magnitude and shape. The spectral magnitude of the endmembers is more difficult to obtain than their spectral shape, in part because the effects of the atmosphere and topography are difficult to constrain. This paper presents a derivative spectral unmixing (DSU) model, which is an extension of the spectral mixture analysis and derivative analysis. Using a DSU approach, it is possible to estimate the fraction of an endmember characterized by one or more diagnostic absorption features despite having only a general knowledge of the spectral shapes of the remaining endmembers. The DSU is assessed using spectral data acquired for a lichen-covered rock sample, and the estimated fractions of lichen and rock are assessed against that obtained from a high spatial resolution digital photograph. The results of the laboratory experiments suggests that the DSU is a promising algorithm for the quantitative analysis of hyperspectral data, but experiments on airborne/spaceborne imagery are now required to assess its value for geological mapping.