The first–quadrant branch (x>0,y>0) of the curve defined implicitly by
ln(xy)=x−y
is under investigation.
(a) Compute dxdy and simplify your result.
(b) Determine all points in the first quadrant where the tangent line is horizontal. Present exact coordinates and justify that no additional horizontal tangents occur within the stated domain.
(c) Determine all points in the first quadrant where the tangent line is vertical. Present exact coordinates and justify that no additional vertical tangents occur within the stated domain.