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

question 124

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) \(- \frac { \sqrt { 3 } } { 12 }\)

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