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Unit 2: Derivatives: definition and basic rules

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Average vs. instantaneous rate of change

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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!

Secant lines

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Secant lines & average rate of change with arbitrary pointsGet 3 of 4 questions to level up!
Secant lines & average rate of change with arbitrary points (with simplification)Get 3 of 4 questions to level up!

Derivative definition

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

Estimating derivatives

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Estimating derivatives
(Opens a modal)

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Estimate derivativesGet 3 of 4 questions to level up!

Differentiability

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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!

Quiz 1

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Power rule

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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!

Derivative rules: constant, sum, difference, and constant multiple

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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!

Combining the power rule with other derivative rules

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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!

Quiz 2

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Derivatives of cos(x), sin(x), 𝑒ˣ, and ln(x)

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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 3 of 4 questions to level up!

Product rule

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

Quotient rule

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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!

Derivatives of tan(x), cot(x), sec(x), and csc(x)

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

Quiz 3

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Proof videos

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Unit test

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