How did you arrive at your answer? What were your steps?

Applying the Product Rule and the Chain Rule, the differentiation would appear to start as:

. . . . .6*(8 cos(8x) (dx/dx))*cos(5y) + 6*(sin(8x))*(-5 cos(5y) sin(5y) (dy/dx)) = 0

. . . . .48 cos(8x) cos(5y) - 30 sin(8x) sin(5y) (dy/dx) = 0

. . . . .48 cos(8x) cos(5y) = 30 sin(8x) sin(5y) (dy/dx)

Divide through to isolate "dy/dx".