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Let f: A R, A R, be a given function and let y = f(x). Let Δx denote a small increment in x. Recall that the increment in y corresponding to the increment in x, denoted by Δy, is given by Δy = f(x + Δx) – f(x). We define the following:
  1. The differential of x, denoted by dx, is defined by dx = Δx.
  2. The differential of y, denoted by dy, is defined by dy = f′(x) dx or 91208.png
In case dx = Δx is relatively small when compared with x, dy is a good approximation of Δy and we denote it by dy ≈ Δy.

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