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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Definitions:

Bulimia Nervosa

An eating disorder marked by binge eating followed by purging, through methods such as vomiting or the use of laxatives, to prevent weight gain.

Binging and Purging

A pattern of eating behavior where excessive food consumption is followed by inappropriate methods to avoid weight gain, often seen in eating disorders.

Eating Disorder

Mental disorders characterized by abnormal or disturbed eating habits that negatively affect a person’s physical or mental health, such as anorexia nervosa, bulimia nervosa, and binge-eating disorder.

DSM-5

The Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition, a comprehensive classification and diagnostic tool used in psychiatry and psychology.