Solve the Problem $\mathrm { f } ( \mathrm { x } , \mathrm { y } ) = \tan ^ { - 1 } \frac { \mathrm { y } } { \mathrm { x } }$

Multiple Choice

Solve the problem.
-Find the derivative of the function $\mathrm { f } ( \mathrm { x } , \mathrm { y } ) = \tan ^ { - 1 } \frac { \mathrm { y } } { \mathrm { x } }$ at the point $( - 3,3 )$ in the direction in which the function increases most rapidly.

A) $\frac { \sqrt { 3 } } { 6 }$
B) $\frac { \sqrt { 3 } } { 9 }$
C) $\frac { \sqrt { 2 } } { 9 }$
D) $\frac { \sqrt { 2 } } { 6 }$