Advanced Derivatives: AP Calculus BC: Free Course

About this course

Advanced differentiation extends familiar rules to implicit relationships, inverses, parametric curves, polar functions and vectors. This course collects those techniques in an AP Calculus BC topic sequence. Study the complete public source playlist from Khan Academy in English, with all 40 recordings in the on-site classroom. Original lesson titles, source order and repeated entries are preserved.

Course at a glance

What you’ll learn

• Differentiate logarithmic, exponential and implicit relationships.
• Find derivatives of inverse functions from tables or equations.
• Work with parametric and vector-valued derivatives.
• Apply differentiation to polar functions.

Skills you’ll gain

• Implicit differentiation
• Inverse functions
• Parametric derivatives
• Polar curves

Course Overview

Exponential and logarithmic derivatives are supported by proofs and by background explanations of the number e. The chain rule links the different representations: an expression may depend on an intermediate variable, a parameter or another implicitly defined quantity. Inverse-function examples use both tables and equations. Parametric and vector-valued recordings add position and second-derivative reasoning, while polar examples apply differentiation to curves described by radius and angle. The retained source includes AB foundations as well as BC extensions. Work with the actual representation in front of you; differentiating a component with respect to a parameter is not automatically the same as finding the slope of the plotted curve.

How to study the course

• Videos 1–10: this part of the source list includes “Second derivatives (vector-valued functions)” through “Worked example: Implicit differentiation”. 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 11–20: this part of the source list includes “Derivative of a parametric function” through “Differentiating using multiple rules: strategy”. 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 21–30: this part of the source list includes “Derivative of ln(x)” through “Derivatives of inverse functions”. 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 31–40: this part of the source list includes “Applying the chain rule twice” through “Derivative of inverse sine”. 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

Compare an explicit function, an implicit relation and a parametric curve. State the independent variable in each case and identify the derivative being requested. Solve one example for each representation, checking a result by an alternative form where possible. Include a second derivative and explain which variable it differentiates with respect to.

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.