Use the Gradient to Find the Directional Derivative of the Function

Multiple Choice

Use the gradient to find the directional derivative of the function at P in the direction of Q. $$g ( x , y ) = x ^ { 2 } + y ^ { 2 } + 1 , \quad P ( 4,8 ) , \quad Q ( 12,24 )$$

A) $- 4 \sqrt { 5 }$
B) $8 \sqrt { 5 }$
C) $16 \sqrt { 5 }$
D) $4 \sqrt { 5 }$
E) $- 8 \sqrt { 5 }$