er calculus derivative of $f$, provided we
      hold every every input variable constant except $x$. We'll
      use the notations $$ \frac{\partial f}{\partial x}, \quad
      \frac{\partial}{\partial x}[f], \quad f_x, \quad \text{ and
      }D_x f $$ to mean the partial of $f$ with respect to
      $x$.</li>

      <li>The partial of $f$ with respect to $y$, written $\ds
      \frac{\partial f}{\partial y}$, $\ds \frac{\partial
      }{\partial y}[f]$, $f_y$, or $D_yf$, is the normal
      first-semester