Differentials

Previously, The derivative was defined as:

(D is the Greek letter delta which implies the difference between two numbers)

The expression dy/dx was never considered before as a quotient of two separate quantities of dy and dx, Differentials allow to give separate meanings to dy and dx in such a way when dx ¹ 0 then dx is equal to the derivative of y with respect to x.

Let y = f(x) be a differentiable function. The differential of x, dx, is any nonzero real number and the differential of y, dy, is defined as

dy = f '(x) dx.