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Rates of change and the concept of derivatives

Use the rule 𝑓′(𝑥) = lim ℎ→0 𝑓(𝑥+ℎ)−𝑓(𝑥) ℎ to determine the derivative of simple power functions and polynomial functions from first principles.

mm-u2-t3-s1-d2

Interactive

From secant to tangent — first principles

manipulative

Shrink h and watch the difference quotient approach f′(x) as the secant falls onto the tangent — first principles for power functions.

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