What does differential mean

Let y = f (x) be defined in the neighborhood of X. x0 and x0 + Δ X are in this interval. If the increment of function Δ y = f (x0 + Δ x) & # 8722; f (x0) can be expressed as Δ y = a Δ x0 + O (Δ x0) (where a is a constant independent of Δ x), and O (Δ x0) is higher order than Δ X

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