Activity: Chain Rule Measurements

Prerequisite concepts

A partial derivative can be expressed in terms of other partial derivatives

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Instructor guide mvpchain

Chain Rule Measurements

This small group activity using surfaces combines practice with the multivariable chain rule while emphasizing numerical representations of derivatives. Students work in small groups to measure partial derivatives in both rectangular and polar coordinates, then verify their results using the chain rule. The whole class wrap-up discussion emphasizes the relationship between a directional derivative in the r-direction and derivatives in x- and y-directions using the chain rule.

Representations used

$\frac{\partial f}{\partial x}$

Inclinometer

Concepts taught

There is a partial derivative in every direction at any point

For a smooth, two dimensional function, a partial derivative can be found at any point and in any direction.