f-a-cylinder">this problem</a>, we
    showed that for a circular cylinder with volume $V=\pi r^2 h$,
    the derivative is $$DV(r,h)=\begin{bmatrix} 2\pi rh &amp; \pi
    r^2 \end{bmatrix}.$$ Suppose that the radius and height are
    both changing with respect to time, where $r=3t$ and $h=t^2$.
    We'll write this parametrically as $\vec g(t) =(3t, t^2)$
    (i.e., $\vec g(t)=(r,h)$).

    <ol>
      <li>In $V=\pi r^2 h$, replace $r$ and $h$ with what they are
      in terms of $t$. Then compute $\dfrac{