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In calculus, an expression based on the derivative of a function, useful for approximating certain values of the function. The differential of an independent variablex, 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 (seelimit), for small values of x, yf(x)x. This formula often enables a quick and fairly accurate approximation to be made for what otherwise would be a tedious calculation.
This entry comes from Encyclopædia Britannica Concise. For the full entry on differential, visit Britannica.com.