{\partial
      y}\frac{dh}{dt}+\frac{\partial f}{\partial z}\frac{dk}{dt}
      .$$ which is equivalent to writing $$\frac{dw}{dt} =
      \frac{\partial f}{\partial x}\frac{dx}{dt}+\frac{\partial
      f}{\partial y}\frac{dy}{dt}+\frac{\partial f}{\partial
      z}\frac{dz}{dt} .$$ [Hint: Rewrite the parametric equations
      for $x$, $y$, and $z$ in vector form $\vec r(t) = (x,y,z)$
      and compute $Dw(x,y,z)$ and $D\vec r(t)$.]</li>

      <li>Suppose that $R=f(V,T,n,P)$, and that $V,T,n,P$ are all
 