tolerances.</p>
                    
                    
                    
                    
                    
                    
  <div class="problem">
    Consider the function $f(x,y) = x^2y +3x+4\sin(5y)$.

    <ol>
      <li>If both $x$ and $y$ depend on $t$, then use implicit
      differentiation to obtain a formula for $df/dt$ in terms of
      $dx/dt$ and $dy/dt$.</li>

      <li>Solve for $df$, and write your answer as the matrix
      product (fill in the question mark) $$df = \begin