 this type of problem until you can compute partial
      derivatives with ease.
    </div>Compute the requested partial and total derivatives.

    <ol>
      <li>For $f(x,y)=x^2+2xy+3y^2$, compute both
      $\ds\frac{\partial f}{\partial x}$ and $f_y$. Then write down 
      $Df(x,y)$.</li>

      <li>For $f(x,y,z)=x^2y^3z^4$, compute $f_x$,
      $\ds\frac{\partial f}{\partial y}$, and $D_z f$. Then write down
      $Df(x,y,z)$.</li>
    </ol>
  </div>When a function has multiple outputs, its partial
  