In calculus, an expression based on the derivative of a function, useful for approximating certain values of the function. The differential of an independent variable x, written x, is an infinitesimal change in its value. The corresponding differential of its dependent variable y is given by y = f(x + x) f(x). Because the derivative of the function f(x), f(x), is equal to the ratio as x approaches zero (see limit), for small values of x, y f(x)x. This formula often enables a quick and fairly accurate approximation to be made for what otherwise would be a tedious calculation.
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