Calculus: Early Transcendentals 8th Edition

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