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 &math.x;, written Δ&math.x;, is an infinitesimal change in its value.
The corresponding differential of its dependent variable &math.y; is given by Δ&math.y; = &math.f;(&math.x; + Δ&math.x;) − &math.f;(&math.x;). Because the derivative of the function &math.f;(&math.x;), &math.f;′(&math.x;), is equal to the ratio Δ&math.y;Δ&math.x; as Δ&math.x; approaches zero (&see; limit), for small values of Δ&math.x;, Δ&math.y; ≅ &math.f;′(&math.x;)Δ&math.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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