Let $X$ be an orthogonal parametrization of some surface $S$. Prove that the Gaussian curvature $K = - \frac{1}{2 \sqrt{E G}} ((\frac{E\_{v}}{\sqrt{E G}})\_{v} + (\frac{G\_{u}}{\sqrt{E G}})\_{u})$, where subscripts denote partial differentiation of the quantity with the subscript with respect to the terms within the subscript, and where $E$, $F$, and $G$ give the first fundamental form of $S$ by $X$.