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 0394; x , is an infinitesimal change in its value. The corresponding differential of its dependent variable y is given by 0394; y /n=/n f (x/n+/n 0394; x)/n-/n f (x). Because the derivative of the function f (x), f 2032; (x), is equal to the ratio 0394; y 0394; x as 0394; x approaches zero (see limit ), for small values of 0394; x , 0394; y /n 2245; /n f 2032; (x) 0394; x . This formula often enables a quick and fairly accurate approximation to be made for what otherwise would be a tedious calculation.