Find the Directional Derivative of the Function at P in the Direction

Multiple Choice

Find the directional derivative of the function at P in the direction of $\overrightarrow { \mathbf { v } } \text {. }$ $f ( x , y , z ) = x y + y z + x z , P ( 1,1,1 ) , \quad \overrightarrow { \mathbf { v } } = 4 \hat { \mathbf { i } } + 5 \hat { \mathbf { j } } - 3 \hat { \mathbf { k } }$

A) $4 / 5 \sqrt { 2 }$
B) $- 8 / 5 \sqrt { 2 }$
C) $12 / 5 \sqrt { 2 }$
D) $24 / 5 \sqrt { 2 }$
E) $- 24 / 5 \sqrt { 2 }$