Contextual applications of differentiation: Free Course

About this course

Study Contextual applications of differentiation in this free English video course from Khan Academy. The classroom preserves all 27 published source recordings, totaling approximately 2h 50m, with their original lesson titles and sequence. The selected curriculum focuses on functions, rates of change, accumulation and mathematical argument. Use the videos to follow an explanation, examine an example and develop a study output you can check independently. The course title describes this recorded subject or learning track; your study can extend beyond watching through the practical activities below.

Course at a glance

What you’ll learn

• Follow the explanation and worked reasoning in “Interpreting the meaning of the derivative in context”, then describe the main idea in your own words.
• Follow the explanation and worked reasoning in “Worked example: Motion problems with derivatives”, then describe the main idea in your own words.
• Follow the explanation and worked reasoning in “Analyzing related rates problems: equations (Pythagoras)”, then describe the main idea in your own words.
• Follow the explanation and worked reasoning in “Related rates: water pouring into a cone”, then describe the main idea in your own words.
• Connect examples across Contextual applications of differentiation by identifying the terms, assumptions and methods they use.
• Create a small independent practice output and check it against the relevant teaching explanation.

Skills you’ll gain

• Function analysis
• Calculus reasoning
• Mathematical notation
• Result verification

Course Overview

The source curriculum is presented as a complete recorded video edition of Contextual applications of differentiation. Representative lessons include “Interpreting the meaning of the derivative in context”, “Analyzing related rates problems: equations (Pythagoras)” and “Proof of special case of l'Hôpital's rule”. These recordings give concrete examples to revisit while building functions, rates of change, accumulation and mathematical argument. Their place in the lesson list is preserved, so you can return to a particular explanation without losing its source position. Introductions, demonstrations, examples, reviews and compilations remain included whenever they appear in the original playlist. Reading a lesson title is useful for locating a topic; working through its reasoning and checking a practice attempt is what makes the recording valuable for learning.

How to study the course

• Videos 1–6: this part of the source list includes “Interpreting the meaning of the derivative in context” through “Worked example: Motion problems with derivatives”. 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 7–13: this part of the source list includes “Applied rate of change: forgetfulness” through “Differentiating related functions intro”. 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 14–20: this part of the source list includes “Worked example: Differentiating related functions” through “Local linearization”. 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 21–27: this part of the source list includes “Local linearity and differentiability” through “Proof of special case of l'Hôpital's 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

Select a representative function or problem from the recordings. Write the conditions, reproduce the method and explain the role of each step. Try another example with a different parameter or interval. Check a symbolic result using a simpler case, a sketch or a numerical comparison when appropriate. Keep track of domains, units and boundary conditions. Finish by explaining what the answer means in the original problem and identify a case in which the same procedure would require extra care.

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.