derivatives will have multiple components, which we write as a
  column vector. For example, if $f(x,y)=(3x^2, \sin(x)+xy)$, then
  $f_x=\left(\begin{matrix}6x\\\cos(x)+y\end{matrix}\right)$. This
  is similar to when we were computing derivatives of space curves,
  for example in <a href=
  "03-Curves.html#derivative-space-curve">this problem</a>.

  <div class="example">
    Let $\vec F(x,y)=(-y^3,2xy)$, a 2D vector field. Then $\vec
    F_x=\begin{bmatrix}0\\2y\end{bmatrix}$, $\vec
    F_y=\begin{bmatrix