Solve the Problem $f ( x , y , z ) = \frac { x } { y } + \frac { y } { z } + \frac { z } { x }$

Multiple Choice

Solve the problem.
-Find the derivative of the function $f ( x , y , z ) = \frac { x } { y } + \frac { y } { z } + \frac { z } { x }$ at the point $( - 7,7 , - 7 )$ in the direction in which the function increases most rapidly.

A) $\frac { 2 } { 7 } \sqrt { 2 }$
B) $\frac { 2 } { 7 } \sqrt { 3 }$
C) $\frac { 3 } { 7 } \sqrt { 2 }$
D) $\frac { 3 } { 7 } \sqrt { 3 }$