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

Multiple Choice

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

A) $\sqrt { 5 }$
B) $\frac { 12 } { \sqrt { 5 } }$
C) 5
D) $- \frac { 5 } { 13 }$
E) $\frac { 78 } { 325 }$