Abstract
ABSTRACT Many students learn the chain rule for differentiation as exactly that - a rule, and even those who use it well often do so with little understanding of why the formula works. This note briefly describes a presentation that introduces students to the chain rule by appealing to their experience with motion. While the presentation does not prove the chain rule, it does convince students that the chain rule makes sense and it provides them with an intuitive understanding of why it works. The note also includes an adaptation of the presentation that helps students understand why we can calculate a definite integral by u-substitution, never returning to the original function or limits of integration.
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