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

Multiple Choice

Solve the problem.
-Find the derivative of the function $f ( x , y ) = \tan ^ { - 1 } \frac { y } { x }$ at the point $( - 4,4 )$ in the direction in which the function decreases most rapidly.

A) $- \frac { \sqrt { 2 } } { 12 }$
B) $- \frac { \sqrt { 3 } } { 8 }$
C) $- \frac { \sqrt { 2 } } { 8 }$
D) $- \frac { \sqrt { 3 } } { 12 }$