$x=2 \rho \sin \phi \cos \theta, y= 2 \rho \sin \phi \sin \theta, z= \rho \cos \phi$ 일 때, 다음 행렬식을 계산하면?

$\displaystyle \begin{vmatrix*}[r] \frac{\partial x} {\partial \rho} & \frac{\partial x} {\partial \theta} & \frac{\partial x} {\partial \phi} \\ \frac{\partial y} {\partial \rho} & \frac{\partial y} {\partial \theta} & \frac{\partial y} {\partial \phi} \\ \frac{\partial z} {\partial \rho} & \frac{\partial z} {\partial \theta} & \frac{\partial z} {\partial \phi} \end{vmatrix*}$

• ①$-2 \rho ^2 \sin \phi$
• ②$-4 \rho ^2 \sin \phi$
• ③$4 \rho ^2 \sin \phi$
• ④$2 \rho ^2 \sin \theta$
• ⑤$4 \rho ^2 \sin \theta$