Okay so I know how to get partial derivatives. One thing that I'm having trouble with is finding f_xy, because I'm not sure if I'm actually doing it correctly.

For example, lets say:

z=xy(5-x)(y-2)

f_x=(5-2x)y(y-2)

f_y=x(5-x)(2y-2)

to my understanding.... to get f_xy you have to take the partial derivative of y and then using that function now take it into respect of x.

So the answer i got was

f_xy=(5-2x)(2y-2)