e second column is $\dfrac{\partial
    f}{\partial v}$.</div>
  </div>
        
        <p>You've now got the key ideas needed to use the chain rule
  in all dimensions. You'll find this shows up many places in
  upper-level math, physics, and engineering courses. The following
  problem will show you how you can use the general chain rule to
  get an extremely quick way to perform implicit differentiation
  from first-semester calculus.</p>

  <div class="problem">
    <div class="marginpar">
      <span 