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Triangular patches interpolation has a number of applications in science and industry, and first-order partial derivatives play an important role in this surface interpolation technology. In this paper a new method for estimating partial derivatives is proposed. The given points are separated into interior points and boundary points, area and shape of base triangles are taken into account for the interior case, and an objective function is structured and minimized for the boundary case. New method is easy to be computed and gets a more accurate result compared with the existing method. Comparison examples are included.