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

question 47

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) \(\frac { \sqrt { 2 } } { 6 }\)

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