The derivative f'(x) of a function f(x) represents the instantaneous rate of change or slope of the function at a particular point x. It is defined as the limit of the difference quotient Δy/Δx as Δx approaches zero:
f'(x) = lim(Δx -> 0) [f(x + Δx) – f(x)] / Δx
Alternatively, the derivative can be defined as the slope of the tangent line to the curve at a particular point.
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