Unpacking the Chain Rule: How to Differentiate Nested Functions
In short: Mastering the chain rule is a cornerstone of calculus. This video walks through a practical example, demonstrating how to differentiate a composite function by breaking it down into its individual components.
The tutorial focuses on the function f(x) = √(3x - x), illustrating how to apply the chain rule because the expression is a composition of two distinct functions: the square root and the linear expression 3x - x. By identifying these layers, students can learn to differentiate complex expressions systematically.
The lesson was created by Sal Khan and features Bill Scott, who uses Khan Academy's materials at Phillips Academy in Andover, Massachusetts. The content is designed for AP Calculus AB students, a curriculum that has been established since the late 1960s.
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Sources
- Summary by Intellect · source: Worked example: Derivative of ÃÂ(3x_-x) using the chain rule | AP Calculus AB | Khan Academy
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