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# Differentiation: definition and basic derivative rules

AP Calc: CHA (BI), CHA‑2 (EU), FUN (BI), FUN‑2 (EU), FUN‑3 (EU)

AP Calc: CHA (BI), CHA‑2 (EU), CHA‑2.A (LO), CHA‑2.A.1 (EK), CHA‑2.B (LO), CHA‑2.B.1 (EK), CHA‑2.B.2 (EK), CHA‑2.B.3 (EK), CHA‑2.B.4 (EK), CHA‑2.C (LO), CHA‑2.C.1 (EK)

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Practice

Secant lines & average rate of changeGet 3 of 4 questions to level up!

Derivative as slope of curveGet 3 of 4 questions to level up!

The derivative & tangent line equationsGet 3 of 4 questions to level up!

AP Calc: CHA (BI), CHA‑2 (EU), CHA‑2.B (LO), CHA‑2.B.2 (EK), CHA‑2.B.3 (EK), CHA‑2.B.4 (EK), CHA‑2.C (LO), CHA‑2.C.1 (EK)

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Practice

Derivative as a limitGet 3 of 4 questions to level up!

AP Calc: CHA (BI), CHA‑2 (EU), CHA‑2.D (LO), CHA‑2.D.1 (EK)

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Estimate derivativesGet 3 of 4 questions to level up!

AP Calc: FUN (BI), FUN‑2 (EU), FUN‑2.A (LO), FUN‑2.A.1 (EK), FUN‑2.A.2 (EK)

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Differentiability at a point: graphicalGet 3 of 4 questions to level up!

Differentiability at a point: algebraicGet 3 of 4 questions to level up!

AP Calc: FUN (BI), FUN‑3 (EU), FUN‑3.A (LO), FUN‑3.A.1 (EK)

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Power rule (positive integer powers)Get 3 of 4 questions to level up!

Power rule (negative & fractional powers)Get 3 of 4 questions to level up!

Power rule (with rewriting the expression)Get 3 of 4 questions to level up!

AP Calc: FUN (BI), FUN‑3 (EU), FUN‑3.A (LO), FUN‑3.A.2 (EK)

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Basic derivative rules: find the errorGet 3 of 4 questions to level up!

Basic derivative rules: tableGet 3 of 4 questions to level up!

AP Calc: FUN (BI), FUN‑3 (EU), FUN‑3.A (LO), FUN‑3.A.3 (EK)

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Practice

Differentiate polynomialsGet 3 of 4 questions to level up!

Differentiate integer powers (mixed positive and negative)Get 3 of 4 questions to level up!

Tangents of polynomialsGet 3 of 4 questions to level up!

AP Calc: FUN (BI), FUN‑3 (EU), FUN‑3.A (LO), FUN‑3.A.4 (EK)

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Derivatives of sin(x) and cos(x)Get 3 of 4 questions to level up!

Derivatives of 𝑒ˣ and ln(x)Get 5 of 7 questions to level up!

AP Calc: FUN (BI), FUN‑3.A (LO), FUN‑3.B (LO), FUN‑3.B.1 (EK)

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Practice

Differentiate productsGet 3 of 4 questions to level up!

Product rule with tablesGet 3 of 4 questions to level up!

AP Calc: FUN (BI), FUN‑3 (EU), FUN‑3.B (LO), FUN‑3.B.2 (EK)

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Practice

Differentiate quotientsGet 3 of 4 questions to level up!

Quotient rule with tablesGet 3 of 4 questions to level up!

Differentiate rational functionsGet 3 of 4 questions to level up!

AP Calc: FUN (BI), FUN‑3 (EU), FUN‑3.B (LO), FUN‑3.B.3 (EK)

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Derivatives of tan(x), cot(x), sec(x), and csc(x)Get 5 of 7 questions to level up!

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### About this unit

The derivative of a function describes the function's instantaneous rate of change at a certain point. Another common interpretation is that the derivative gives us the slope of the line tangent to the function's graph at that point. Learn how we define the derivative using limits. Learn about a bunch of very useful rules (like the power, product, and quotient rules) that help us find derivatives quickly.AP® is a registered trademark of the College Board, which has not reviewed this resource.