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Given the example [itex]g = \frac{GM}{R^{2}}[/itex], we may compute the change in field strength if the mass is changed by a small amount dM to be$$dg = \frac{G dM}{R^{2}}$$and also if R is changed by dR,$$dg = \frac{-2 GM dR}{R^{3}}$$If, however, both the mass and radius are changed by a small amount at the same time, the source I'm using states that the overall change in field strength is simply the sum:$$dg = \frac{G dM}{R^{2}} - \frac{2 GM dR}{R^{3}}$$I was wondering if anyone could explain why this is a valid step. Thank you!