Skip to content

Learn Practice Plan Tutors Ask AI

⌘K

Sign in Join freeGet started

Courses Lessons Quick lessons Merit Tutors' Videos

Loading

Every AP course and the SAT, with the best lessons, Merit AI, and a plan for every test.

Learn

Courses
Lessons
Quick lessons
Merit Tutors' Videos
Merit AI

Study

Exam Sprint
Quick session
Learning plan
My schedule
Progress

Tutoring

Find a tutor
Become a tutor
Partner with Merit
For teachers

Merit

About
Pricing
For parents
How ranking works
Privacy
Terms

Videos play on YouTube. AP® and SAT® are trademarks of the College Board, which is not affiliated with Merit.

© 2026 Merit

Learn Practice Plan Ask AI

AP Calculus AB›Unit 2: Differentiation: Definition and Fundamental Properties›The derivative

The Definition of the Derivative

The derivative is the limit of the difference quotient. It gives the slope of the tangent line and the instantaneous rate of change.

The limit definition
Notation: f′(x), dy/dx
Tangent line equations

Master this topicQuick session · about 18 min

Watch the top lessonMath with Professor V Find a tutor

Search Calc AB

Quiz coming up?Connect your calendar: Merit preps you for every quiz and test.Sign up and connect

1 videos ranked by how well they teach

1

Calculus 1: The Tangent and Velocity Problems (Video #1) | Math with Professor V

126K views on YouTube · 6 years ago

Math with Professor V

Calc BC · The Definition of the Derivative

More lessons from Unit 2: Differentiation: Definition and Fundamental Properties

The best-ranked videos for the rest of this unit.

Finding The Tangent Line Equation With Derivatives - Calculus Problems

2.3M views on YouTube · 10 years ago

The Organic Chemistry Tutor

Calc BC · The Power Rule

Differentiation Formulas - Notes

1.4M views on YouTube · 3 years ago

The Organic Chemistry Tutor

Calc BC · The Power Rule

❖ Basic Derivative Rules - The Shortcut Using the Power Rule , 3 Examples ❖

973K views on YouTube · 14 years ago

Calc BC · The Power Rule

Implicit Differentiation - Find The First & Second Derivatives

794K views on YouTube · 7 years ago

The Organic Chemistry Tutor

Calc BC · The Power Rule

The Power Rule For Derivatives

764K views on YouTube · 8 years ago

The Organic Chemistry Tutor

Calc BC · The Power Rule

Power rule | Derivative rules | AP Calculus AB | Khan Academy

634K views on YouTube · 13 years ago

Calc BC · The Power Rule

Derivatives - Power Rule

231K views on YouTube · 10 years ago

The Organic Chemistry Tutor

Calc BC · The Power Rule

The Power Rule - Fraction Examples - Derivatives Calculus

206K views on YouTube · 13 years ago

Calc BC · The Power Rule

Derivatives of Trigonometric Functions

193K views on YouTube · 8 years ago

Professor Dave Explains

Calc BC · The Power Rule

Derivatives of Polynomial Functions: Power Rule, Product Rule, and Quotient Rule

171K views on YouTube · 8 years ago

Professor Dave Explains

Calc BC · The Power Rule

Justifying the power rule | Derivative rules | AP Calculus AB | Khan Academy

154K views on YouTube · 13 years ago

Calc BC · The Power Rule

Calculus AB/BC – 2.5 Applying the Power Rule

118K views on YouTube · 6 years ago

Calc BC · The Power Rule

Quiz on The Definition of the Derivative soon?

Connect your class calendar and Merit lines up the lessons for every quiz and test, days before it's due.

Works with Canvas, Schoology, Blackbaud, Google Classroom, and more.

Sign up and connect

2Differentiation: Definition and Fundamental Properties

Average and Instantaneous Rates of Change
The Definition of the Derivative
Estimating Derivatives from Graphs and Tables
Differentiability and Continuity
The Power Rule
Derivatives of sin x, cos x, eˣ, and ln x
Product and Quotient Rules
Derivatives of tan, cot, sec, and csc

Next topic

Estimating Derivatives from Graphs and Tables

209daysGet the Calc AB score you want.Free diagnostic, then a day-by-day Exam Sprint to exam day.

Best teachers for this topic

1Math with Professor V

Get a Calc AB tutor

Teacher? Add a lesson or guide for this topic

Also called: definition of derivative, limit definition of derivative, derivative notation, tangent line