Solve the Problem $- \frac { 5 } { 34 } \sqrt { 2 }$

Multiple Choice

Solve the problem.
-Find the derivative of the function f(x, y, z) = ln(xy + yz + zx) at the point (-2, -4, -6) in the direction in which the function decreases most rapidly.

A) $- \frac { 5 } { 34 } \sqrt { 2 }$
B) $- \frac { 5 } { 26 } \sqrt { 2 }$
C) $- \frac { 5 } { 14 } \sqrt { 2 }$
D) $- \frac { 5 } { 22 } \sqrt { 2 }$