# Taking derivatives

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Lessons

Introduction to differential calculusDerivative as slope of tangent lineDerivative as instantaneous rate of changeQuiz 1Secant linesDerivative as a limitFormal definition of derivativeUsing the formal definition of derivativeQuiz 2DifferentiabilityDerivative as a functionQuiz 3Review: Derivative basicsBasic differentiation rulesPower ruleQuiz 4Polynomial functions differentiationRational functions differentiation (intro)Quiz 5Radical functions differentiation (intro)Sine & cosine derivativesQuiz 6eˣ and ln(x) derivativesReview: Basic differentiationQuiz 7Product ruleChain ruleChain rule proofQuiz 8Quotient ruleReview: Product, quotient, & chain ruleRational functions differentiationQuiz 9Radical functions differentiationTrigonometric functions differentiationQuiz 10Exponential functions differentiationLogarithmic functions differentiationQuiz 11Derivatives capstoneImplicit differentiation introductionImplicit differentiation (advanced examples)Inverse trig functions differentiationQuiz 12Derivatives of inverse functionsDisguised derivativesProofs for the derivatives of eˣ and ln(x)Logarithmic differentiationQuiz 13Parametric & vector-valued function differentiationReview: Advanced differentiationHigher-order derivativesQuiz 14Higher-order derivatives (parametric & vector-valued functions)Polar curve differentiationUnit testPractice

Quizzes

Unit test

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Secant lines & average rate of change with arbitrary points

4 questions

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Derivative as a limit: numerical

4 questions

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Differentiability at a point: graphical

4 questions

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Differentiability at a point: algebraic

4 questions

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Visualizing derivatives

4 questions

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Derivatives basics challenge

7 questions

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Differentiating linear functions

4 questions

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Basic differentiation rules

4 questions

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Polynomial functions differentiation

4 questions

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Tangents of polynomials

4 questions

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Fractional powers differentiation

4 questions

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Radical functions differentiation intro

4 questions

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Special derivatives quiz

5 questions

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Basic differentiation challenge

7 questions

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Power rule challenge

7 questions

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Common derivatives challenge

7 questions

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Differentiate composite functions

4 questions

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Chain rule with tables

4 questions

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Product, quotient, & chain rules challenge

4 questions

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Radical functions differentiation

4 questions

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Exponential functions differentiation intro

4 questions

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Exponential functions differentiation

4 questions

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Logarithmic functions differentiation intro

4 questions

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Logarithmic functions differentiation

4 questions

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Differentiating using multiple rules

4 questions

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Tangents & normal lines challenge

4 questions

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Disguised derivatives

4 questions

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Advanced differentiation challenge

4 questions

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Second derivatives

4 questions

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Tangents to polar curves

4 questions

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**Taking derivatives**with these 15 questions.About this unit

The big idea of differential calculus is the concept of the derivative, which essentially gives us the direction, or rate of change, of a function at any of its points. Learn all about derivatives and how to find them here.