Find the Directional Derivative of the Function $f ( x , y , z ) = \sqrt { x y z }$

Multiple Choice

Find the directional derivative of the function $f ( x , y , z ) = \sqrt { x y z }$ at the point $( 2,4,2 )$ in the direction of the vector $\{ 4,2 , - 4 \}$ .

A) $- \frac { 1 } { 6 }$


B) $- \frac { 1 } { 4 }$
C) $- \frac { 1 } { 2 }$
D) 0
E) $\frac { 1 } { 2 }$
F) $\frac { 1 } { 4 }$

G) $\frac { 1 } { 6 }$
H) $\frac { 1 } { 8 }$