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====== 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 [[strategy:smallwhiteboard:|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.


{{swbq:insw:inswconstant.ppt|Powerpoint slide}}
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{{swbq:insw:inswconstant.pdf|PDF slide}}


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