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MathCalculus

The Rate of Change of y with Respect to x Is the Derivative

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Question

Complete the statement: The instantaneous rate of change of yy with respect to xx is the ________ of yy with respect to xx.

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Evidence boundary

The blank is answered as an instantaneous rate of change. The derivative exists only at points where the defining limit exists. Over a finite interval, Δy/Δx is an average rate of change rather than the derivative at one point.