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 Δ x , is an infinitesimal change in its value. The corresponding differential of its dependent variable y is given by Δ y /n=/n f (x/n+/nΔx)/n-/n f (x). Because the derivative of the function f (x), f ′(x), is equal to the ratio Δ y Δ x as Δ x approaches zero (see limit ), for small values of Δ x , Δ y /n≅/n f ′(x)Δ x . This formula often enables a quick and fairly accurate approximation to be made for what otherwise would be a tedious calculation.
[c mediumvioletred] (as used in expressions)
ordinary differential equation
partial differential equation