MathematicsGeneralQuality 76 · Exceptional

What a Derivative Really Means

@author · 2026-07-14 · v1

7 min read

A derivative measures the rate of change at an instant. For

f(x) = x^2

, the derivative

f'(x) = 2x

tells you how steep the curve is at any point. At

x = 3

, the slope is 6 — meaning the function rises 6 units for every 1 unit of horizontal change right there.

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