Question part points submissions used find dy/dx by implicit differentiation. x sin(y) + y sin(x) = 2

Using the product rule
xCos(y)dy/dx + sin(y) + ycos(x)+sin(x)dy/dx = 0
xcosydy/dx + sin(x)dy/dx = -sin(y) - ycos(x)
(xcos(y) + sin(x))dy/dx = -sin(y) - ycos(x)
dy/dx = [-sin(y) - ycos(x)]/ {xcos(y) + sin(x)}