Find the Jacobian of the Transformation $x = \rho \sin \phi \cos \theta$

Find the Jacobian of the transformation $x = \rho \sin \phi \cos \theta$ , $y = \rho \sin \phi \sin \theta$ , $z = \rho \cos \phi$ .

A) $\theta$
B) $\beta ^ { 2 } \sin \phi$
C) $\rho \sin \phi$
D) $\rho ^ { 2 } \cos \phi$
E) 2 $\theta$
F) $\rho ^ { 2 } \sin \theta$
G) $\rho \sin \theta$
H) $\rho \cos \phi$

Correct Answer:

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