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Unit: Derivatives introduction

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Possible mastery points

The derivative: An intuitive introduction

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Practice

Derivative as slope of curveGet 3 of 4 questions to level up!
Derivative & the direction of a functionGet 3 of 4 questions to level up!

Estimating derivatives with secant lines and average rate of change

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

Quiz 1

Level up on the above skills and collect up to 320 Mastery points

Secant lines & average rate of change with arbitrary points

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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!

Formal definition of the derivative as a limit

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Derivative as a limitGet 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!

Tangent lines and local linearity

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The derivative & tangent line equationsGet 3 of 4 questions to level up!
Approximation with local linearityGet 3 of 4 questions to level up!

Optional videos

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Proof: Differentiability implies continuity
(Opens a modal)

Quiz 2

Level up on the above skills and collect up to 560 Mastery points

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Unit test

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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 these two interpretations describe the same thing and how we can define the derivative formally using... limits!