larsonfive">See Larson 13.5:27&ndash;30 for more
      practice, and see pages 929&ndash;930 for how the book derives
      these formulas.</span>
    </div>
      Suppose $z=f(x,y)$. If $z$ is held constant, this
    produces a level curve. As an example, if $f(x,y) =
    x^2+3xy-y^3$ then $5=x^2+3xy-y^3$ is a level curve. Our goal in
    this problem is to find $dy/dx$ in terms of partial derivatives
    of $f$.

    <ol>
      <li>Suppose $x=x$ and $y=y(x)$, so $y$ is a function of $x$.
      We can writ