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We compare the performance of two procedures used for the evaluation of uncertainty of derivatives computed from a polynomial fitted to experimental data. These procedures agree with international recommendations and they are valid independently of the experimental technique used to obtain the data. The first procedure involves performing a least-squares polynomial adjustment under uncertainty. The second procedure is based on Monte Carlo techniques. Both are computer-assisted. As an example, we evaluated the standard uncertainty associated with the gradient of a surface fitted to experimental data that formed a set of points in a three-dimensional space. We found that both methods render very similar results.