Comparison of derivative operators via quantitative performance analysis is rarely addressed in medical imaging. Indeed, the main application of such operators is the extraction of edges and, since there is no unequivocal definition of edges, the common trend is to identify the best performing operator based on a qualitative match between the extracted edges and the fickle human perception of object boundaries. This study presents an objective comparison of four first-order derivative operators through quantitative analysis of results yielded in a specific task, i.e. a spine kinematics application. Such application is based on a template matching method, which estimates common kinematic parameters of intervertebral segments from an X-ray fluoroscopy sequence of spine motion, by operating on the image derivatives of each frame. Therefore, differences in image derivatives, computed via different derivative operators, may lead to differences in estimated parameters of intervertebral kinematics. The comparison presented in this study focused on the trajectory of the instantaneous center of rotation (ICR) of an intervertebral segment, as it is particularly sensitive even to very small differences in displacements and velocities. Therefore, a quantitative analysis of the discrepancies between the ICR trajectories, obtained with each of the four considered derivative operators, was carried out by defining quantitative measures. The results showed detectable differences in the obtained ICR trajectories, thus highlighting the need for quantitative analysis of derivative operator performances in applications aimed at providing quantitative results. However, the significance level of such differences for clinical applications should be further assessed, but, currently, it is not possible, as there is no consensus and sufficient data on kinematic parameters features associated with specific spinal pathologies.