e Geometry of Derivatives</h1>
<section>
  <h1>Tangent planes of $z=f(x,y)$</h1>
    
    
    <p>We promised earlier in this
  chapter that you can obtain most of the results in multivariate
  calculus by replacing the $x$ and $y$ in $dy=f'dx$ with $\vec x$
  and $\vec y$. Let's review how to find the tangent line for
  functions of the form $y=f(x)$, and then generalize to finding
  tangent planes for functions of the form $z=f(x,y)$.</p>

  <div class="problem" label="Tangent Lines">
    Consider the fun