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 $( 3,4 )$ in the direction in which the function decreases most rapidly.

A) $- 3 \sqrt { 26 }$
B) $- \sqrt { 221 }$
C) $- \sqrt { 173 }$
D) $- \sqrt { 167 }$