Let $f ( x , y , z ) = x ^ { 2 } y - x y z ^ { 2 }$

Multiple Choice

Let $f ( x , y , z ) = x ^ { 2 } y - x y z ^ { 2 }$ . Then the directional derivative of f at $P = ( 0,1,2 )$ in the direction of the unit vector $\mathbf { U }$ which is parallel to $\overrightarrow { P Q }$ where $Q = ( 1,4,3 )$ is

A) $\frac { \sqrt { 3 } + 1 } { 2 }$
B) $- \frac { 4 } { \sqrt { 26 } }$
C) $\frac { - 4 + 5 \sqrt { 3 } } { 2 }$
D) $- \frac { 5 } { 13 }$
E) $\frac { 78 } { 325 }$