 calculus derivative of $f$ assuming that $y$ is the only variable changing (all other variables are constant). A similar
      definition holds for partial derivatives with respect to any
      variable.</li>

      <li>
The derivative of $f$ is a matrix. The columns of
        the derivative are the partial derivatives. When there's
        more than one input variable, we'll use the notation $Df$ rather than
        $f'$ for the derivative. The order of the columns
        must match the order of the var