Vi får \[ J= \left| \begin{array}{cc} \frac{\partial x}{\partial u} & \frac{\partial x}{\partial v}\\ \frac{\partial y}{\partial u} & \frac{\partial y}{\partial v} \end{array} \right| = \left| \begin{array}{cc} \frac{1}{2\sqrt{uv}} & -\frac{\sqrt{u}}{2v^{3/2}}\\ \frac{\sqrt{v}}{2\sqrt{u}} & \frac{\sqrt{u}}{2\sqrt{v}} \end{array} \right| =\frac{1}{2v}. \] Jämför nästa avsnitt.