Table of Contents

Drawing Functions of Several Variables

The Prompt

Given that $x=x(u,v)=u$ and $y=y(u,v)=\frac{1}{2}u+3v,$ draw lines of u equals constant and v equals constant.

Context

Use this SWBQ as a preliminary to a discussion about the fact that it matters what you are holding constant in a partial derivative.

Wrap Up

Ask students to discuss the difference between the two partial derivatives: $$\left(\frac{df}{dx}\right)_y \qquad\qquad \left(\frac{df}{dx}\right)_u$$ They should be able to discuss these two derivatives in terms of their graph from the SWBQ.

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