Solve the Problem $\frac { 5 } { 88 } \sqrt { 2 }$

Multiple Choice

Solve the problem.
-Find the derivative of the function f(x, y, z) = ln(xy + yz + zx) at the point (8, 16, 24) in the direction in which the function increases most rapidly.

A) $\frac { 5 } { 88 } \sqrt { 2 }$
B) $\frac { 5 } { 56 } \sqrt { 2 }$
C) $\frac { 5 } { 104 } \sqrt { 2 }$
D) $\frac { 5 } { 136 } \sqrt { 2 }$