When changing from Cartesian to spherical coordinates, $\frac { \partial \phi } { \partial x } =$
A) $- \sin \phi / ( r \sin \theta )$
B) $\sin \phi / ( r \sin \theta )$
C) $- \cos \phi / ( r \sin \theta )$
D) $\cos \phi / ( r \cos \theta )$
E) $\sin \phi / ( r \cos \theta )$

Question

Quizplus · Accepted Answer

The partial derivative $\frac{\partial \phi}{\partial x}$ in spherical coordinates is $-\sin \phi / (r \sin \theta)$ because $\phi$ is the azimuthal angle, and its change with respect to $x$ involves the sine of $\phi$ and the radius $r$ and polar angle $\theta$.

When Changing from Cartesian to Spherical Coordinates ∂ϕ∂x=\frac { \partial \phi } { \partial x } =∂x∂ϕ​=

When Changing from Cartesian to Spherical Coordinates $\frac { \partial \phi } { \partial x } =$