Answer
$1, \lt 0,1 \gt$
Work Step by Step
Formula to calculate the maximum rate of change of $f$: $D_uf=|\nabla f(x,y)|$
$\nabla f(x,y)=\lt y \cos xy,x\cos xy \gt $
$\nabla f(1,0)=\lt 0,\cos (0) \gt=\lt 0,1 \gt$
$|\nabla f(0,1)|=\sqrt{0^2+ 1^2}=1$
Hence, the required answers are:
$1, \lt 0,1 \gt$
