Use implicit differentiation to find dy/dxdy/dxdy/dx for ex+y=xye^{x+y} = xyex+y=xy.
y−ex+yex+y−x\frac{y - e^{x+y}}{e^{x+y} - x}ex+y−xy−ex+y
ex+y−yx−ex+y\frac{e^{x+y} - y}{x - e^{x+y}}x−ex+yex+y−y
Both (a) and (c)