In calculus, the differential represents the principal part of the change in a function y = ƒ(x) with respect to changes in the independent variable. The differential dy is defined by:

dy=f '(x)*dx

where f'(x) is the derivative of ƒ with respect to x, and dx is an additional real variable (so that dy is a function of x and dx). The notation is such that the equation:

dy=(dy/dx)*dx

holds, where the derivative is represented in the Leibniz notation dy/dx, and this is consistent with regarding the derivative as the quotient of the differentials. One also writes:

df(x)=f '(x)*dx

The precise meaning of the variables dy and dx depends on the context of the application and the required level of mathematical rigor.

See also, if You wish: Derivative of a Function.

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