Answer
True
Work Step by Step
Given: $f(x,y)=sinx+siny$
Take derivative.
$D_{u}(x,y)=cosx+cosy$
Since, $D_{u}(x,y) \leq |∇ f(x,y)| =|cosx+cosy|$
$=\sqrt {cos^{2}x+cos^{2}y}\leq \sqrt {1+1}=\sqrt 2$
Hence, the given statement is true.