Solve the Problem $f ( x , y ) = x ^ { 2 } + x y + y ^ { 2 }$

Multiple Choice

Solve the problem.
-Find the derivative of the function $f ( x , y ) = x ^ { 2 } + x y + y ^ { 2 }$ at the point $( 4,5 )$ in the direction in which the function increases most rapidly.

A) $\sqrt { 293 }$
B) $3 \sqrt { 42 }$
C) $\sqrt { 299 }$
D) $\sqrt { 365 }$