If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Main content

Unit 2: Differentiation: definition and basic derivative rules

2,300 possible mastery points

Mastered

Proficient

Familiar

Attempted

Not started

Quiz

Unit test

About this unit

The derivative of a function describes the function's instantaneous rate of change at a certain point - it gives us the slope of the line tangent to the function's graph at that point. See how we define the derivative using limits, and learn to find derivatives quickly with the very useful power, product, and quotient rules.

Defining average and instantaneous rates of change at a point

Learn

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!

Defining the derivative of a function and using derivative notation

Learn

Practice

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

Estimating derivatives of a function at a point

Learn

Estimating derivatives
(Opens a modal)

Practice

Estimate derivativesGet 3 of 4 questions to level up!

Connecting differentiability and continuity: determining when derivatives do and do not exist

Learn

Practice

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

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

Applying the power rule

Learn

Practice

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: introduction

Learn

Practice

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

Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule

Learn

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!

Quiz 2

Level up on the above skills and collect up to 640 Mastery points

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

Learn

Practice

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!

The product rule

Learn

Practice

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

The quotient rule

Learn

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!

Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions

Learn

Practice

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

Quiz 3

Level up on the above skills and collect up to 640 Mastery points

Optional videos

Learn

Up next for you:

Unit test

Level up on all the skills in this unit and collect up to 2300 Mastery points!

AP® is a registered trademark of the College Board, which has not reviewed this resource.