Provide an Appropriate Answer $x ^ { 2 } + y ^ { 2 } = r ^ { 2 }$

Multiple Choice

Provide an appropriate answer.
-Suppose that $x ^ { 2 } + y ^ { 2 } = r ^ { 2 }$ and $x = r \cos \theta$ , as in polar coordinates. Find $\left( \frac { \partial y } { \partial \theta } \right) _ { r }$ .

A) $\left( \frac { \partial y } { \partial \theta } \right) _ { r } = - r \sin \theta$
B) $\left( \frac { \partial y } { \partial \theta } \right) _ { r } = r \cos \theta$
C) $\left( \frac { \partial y } { \partial \theta } \right) _ { r } = r ( \cos \theta - \sin \theta )$
D) $\left( \frac { \partial y } { \partial \theta } \right) _ { \mathrm { r } } = 0$