 can quickly be
  developed from differential notation. Once we have the language
  of vectors and matrices at our command, we will develop calculus
  in higher dimensions by writing $d\vec y = Df(\vec x) d\vec x$.
  Variables will become vectors, and the derivative will become a
  matrix. This problem will help you see how the notion of
  differentials is used to develop equations of tangent lines.
  We'll use this same idea to develop tangent planes to surfaces in
  3D and more.</p>

  <div class="problem