HW$3$: Problem $6$

$(10$ points$)$

Calculate all four second$-$order partial derivatives and check that $f_{zy}=f_{yx}.$ Assume the variables are restricted to a domain on which the function is defined.

$f(x,y)=2sin(2x)cos(2y)$

$6$

$8$

$6$

Note: You can earn partial credit on this problem.