Introduction to derivatives lesson for Calculus with guided notes, homework, and video lesson. Teach the tangent line problem, definition of derivative, derivative notation, and tangent and normal lines.

This is one lesson from my Calculus Unit 2 – Derivatives and Applications curriculum. It includes guided notes, homework practice, a full video lesson, and detailed step-by-step answer keys to support student understanding.

This lesson is designed for a guided, non-AP Calculus course and works well for honors-level high school calculus or introductory calculus classes. The structure builds from evaluating functions and the difference quotient to understanding derivatives as slopes of tangent lines.

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💜 Topics Covered in This Lesson

• Quick review of evaluating functions

• Difference quotient

• Finding the equation of a tangent line to a circle

• Tangent line problem

• Finding the slope of secant and tangent lines

• Definition of derivative

• Derivative notation

• Equations of tangent lines

• Equations of normal lines

💜 What’s Included

• Guided notes

• Homework practice (12+ problems)

• 14+ worked examples

• Full video lesson (walks through notes and examples)

• Detailed step-by-step answer key

💜 Perfect For

• High school Calculus

• Honors Calculus

• Introductory Calculus

• Non-AP Calculus courses

• Derivatives units

• Teachers who want structured, guided instruction with video support

This lesson is designed to make introducing derivatives more clear, organized, and manageable while helping students understand the connection between slopes, tangent lines, and rates of change.

I have been teaching high school math, mostly honors-level courses, in the private school system for over 25 years. After much success with my digital Algebra 2 curriculum with videos, I decided to create a non-AP Calculus curriculum with guided notes, video lessons, homework practice, and detailed answer keys to use with my own students and share with other teachers.

I hope this resource helps make teaching Calculus clearer, smoother, and more manageable for you and your students!

-Shira Strong

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