uce the vocabulary in terms
  of the problem above, and then make a formal definition.</p>

  <ul>
    <li>The derivative of $f$ in the previous problem is the matrix
    $$Df(x,y) = \begin{bmatrix} 2xy+3&amp; x^2+20\cos(5y)
    \end{bmatrix}.$$ Some people call $Df$ the <em>total
    derivative</em> or the <em>matrix derivative</em> of $f$.</li>

    <li>The first column of this matrix is just part of the whole
    derivative&mdash;the part that deals with how changes in $x$ affect
    the output. We can g