Find the Directional Derivative of the Function $f ( x , y ) = x ^ { 2 } + y ^ { 2 }$

Multiple Choice

Find the directional derivative of the function $f ( x , y ) = x ^ { 2 } + y ^ { 2 }$ at the point $( 1,1 )$ in the direction $\theta = \frac { \pi } { 4 }$ .

A) $\sqrt { 2 }$
B) $2 \sqrt { 2 }$
C) $4 \sqrt { 2 }$
D) $\frac { 1 } { \sqrt { 2 } }$
E) 1
F) 2
G) 4
H)
$\frac { 1 } { 2 }$