Introduction to Derivatives: Free Course

About this course

A derivative describes instantaneous change by examining nearby average changes. This introductory course develops secant lines, tangent slopes, derivative definitions and differentiability. Study the complete public source playlist from Khan Academy in English, with all 24 recordings in the on-site classroom. Original lesson titles, source order and repeated entries are preserved.

Course at a glance

What you’ll learn

• Interpret secant and tangent slopes as rates of change.
• Use limit definitions to calculate a derivative.
• Construct tangent lines and local linear approximations.
• Distinguish continuity from differentiability.

Skills you’ll gain

• Derivative definition
• Tangent lines
• Differentiability
• Local linearization

Course Overview

The recordings move between graphical intuition and algebraic limits. Secant-line examples vary one point or the difference between inputs, showing how an average rate approaches a tangent slope when the relevant limit exists. Formal and alternate derivative definitions are applied to specific functions, including a square and a logarithm. Tangent-line equations and local linearization connect the derivative with approximation. Differentiability examples distinguish smooth local behavior from points where a derivative fails to exist, and a proof relates differentiability to continuity. Keep the derivative at one point distinct from the derivative function that assigns a rate across a domain.

How to study the course

• Videos 1–6: this part of the source list includes “Slope of a secant line example 1” through “Formal and alternate form of the derivative”. Identify the function, variable and conditions. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 7–12: this part of the source list includes “Newton, Leibniz, and Usain Bolt” through “Derivative as slope of curve”. Connect the method to the meaning of the problem. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 13–18: this part of the source list includes “Secant line with arbitrary point (with simplification)” through “Local linearity and differentiability”. Rework a demonstration with a changed parameter. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 19–24: this part of the source list includes “Estimating derivatives” through “Differentiability and continuity”. Check the result and explain its interpretation. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits learners with algebra and trigonometry preparation who want the specific calculus topic in the title. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

Comfort manipulating algebraic expressions and interpreting functions is important. Review the prerequisite calculus stated by a lesson before using an advanced technique.

Put the lessons into practice

For a simple polynomial, calculate average rates over shrinking intervals and compare them with the derivative at a point. Derive that value from the limit definition, then write the tangent line. Use it for a nearby approximation and explain why the approximation should not automatically be trusted far from the point.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.