Derivative Rules: Free Course

About this course

Derivative rules turn the limit definition into a practical calculation toolkit. This course develops power, product, quotient and chain rules with proofs, examples and error analysis. Study the complete public source playlist from Khan Academy in English, with all 45 recordings in the on-site classroom. Original lesson titles, source order and repeated entries are preserved.

Course at a glance

What you’ll learn

• Apply power, product, quotient and chain rules.
• Differentiate polynomial, rational, radical and trigonometric functions.
• Use tabulated function and derivative values.
• Identify and explain common differentiation errors.

Skills you’ll gain

• Derivative rules
• Chain rule
• Trigonometric derivatives
• Error analysis

Course Overview

Polynomial, rational, radical and trigonometric functions supply the main examples. Rewriting an expression can make its structure easier to differentiate, but products, quotients and compositions still require the appropriate rule. Tables provide derivative information without an explicit formula, and tangent-line examples connect the result with a graph. Proofs revisit why the rules work, including trigonometric limits and the relationship between differentiability and continuity. Find-the-error recordings make omitted factors and mistaken rule combinations visible. The useful habit is to identify the expression's structure before calculating, then check whether every factor and dependency has been accounted for.

How to study the course

• Videos 1–11: this part of the source list includes “Differentiating polynomials example” through “y-intercept of tangent line example”. 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 12–22: this part of the source list includes “Chain rule proof” through “Basic derivative rules (Part 1)”. 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 23–33: this part of the source list includes “Proof of the derivative of cos(x)” through “Power rule”. 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 34–45: this part of the source list includes “Proof: d/dx(x^n)” through “Worked example: Derivative of cos_(x) using the chain rule”. 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

Prepare one example each for a product, quotient and composition. Annotate the structure before differentiating and explain why the chosen rule applies. Solve a table-based derivative question, then inspect a deliberately incorrect solution and identify the missing factor or invalid step. Check a simple result with the derivative definition or an equivalent form.

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.