# Taking derivatives

Lessons

Introduction to differential calculusDerivative as slope of tangent lineDerivative as instantaneous rate of changeSecant linesDerivative as a limitFormal definition of derivativeUsing the formal definition of derivativeDifferentiabilityDerivative as a functionReview: Derivative basicsBasic differentiation rulesPower rulePolynomial functions differentiationRational functions differentiation (intro)Radical functions differentiation (intro)Sine & cosine derivativeseˣ and ln(x) derivativesReview: Basic differentiationProduct ruleChain ruleChain rule proofQuotient ruleReview: Product, quotient, & chain ruleRational functions differentiationRadical functions differentiationTrigonometric functions differentiationExponential functions differentiationLogarithmic functions differentiationDerivatives capstoneImplicit differentiation introductionImplicit differentiation (advanced examples)Inverse trig functions differentiationDerivatives of inverse functionsDisguised derivativesProofs for the derivatives of eˣ and ln(x)Logarithmic differentiationParametric & vector-valued function differentiationReview: Advanced differentiationHigher-order derivativesHigher-order derivatives (parametric & vector-valued functions)Polar curve differentiationPractice

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Practice

Secant lines & average rate of change with arbitrary points

4 questions

Practice

Practice

Derivative as a limit: numerical

4 questions

Practice

Learn

Learn

Practice

Differentiability at a point: graphical

4 questions

Practice

Differentiability at a point: algebraic

4 questions

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Practice

Visualizing derivatives

4 questions

Practice

Practice

Derivatives basics challenge

7 questions

Practice

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Practice

Differentiating linear functions

4 questions

Practice

Basic differentiation rules

4 questions

Practice

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Practice

Polynomial functions differentiation

4 questions

Practice

Tangents of polynomials

4 questions

Practice

Practice

Fractional powers differentiation

4 questions

Practice

Radical functions differentiation intro

4 questions

Practice

Practice

Special derivatives quiz

5 questions

Practice

Practice

Basic differentiation challenge

7 questions

Practice

Power rule challenge

7 questions

Practice

Common derivatives challenge

7 questions

Practice

Learn

Learn

Practice

Differentiate composite functions

4 questions

Practice

Chain rule with tables

4 questions

Practice

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Practice

Product, quotient, & chain rules challenge

4 questions

Practice

Practice

Radical functions differentiation

4 questions

Practice

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Practice

Exponential functions differentiation intro

4 questions

Practice

Exponential functions differentiation

4 questions

Practice

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Practice

Logarithmic functions differentiation intro

4 questions

Practice

Logarithmic functions differentiation

4 questions

Practice

Learn

Practice

Differentiating using multiple rules

4 questions

Practice

Tangents & normal lines challenge

4 questions

Practice

Practice

Disguised derivatives

4 questions

Practice

Practice

Advanced differentiation challenge

4 questions

Practice

Practice

Second derivatives

4 questions

Practice

Practice

Tangents to polar curves

4 questions

Practice

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.