 depend on
      $t$ (not $x$ or $y$)?</li>

      <li>The chain rule states that $D(f\circ \vec r)(t) = Df(\vec
      r(t))D\vec r(t)$. Explain why we write $Df(\vec r(t))$
      instead of $Df(x,y)$.</li>
    </ol>If you'd like to make sure you are correct, try the
    following: replace $x$ and $y$ in $f=x^2+xy$ with what they are
    in terms of $t$, and then just use first-semester calculus to
    find $df/dt$. Is it the same?
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