#y^2=2+xy#

#rarr color(white)("XX")y^2-xy=2#

#rarr color(white)("XX")(d(y^2-xy))/(dx)=(d (2))/(dx)#

#rarr color(white)("XX")(d(y^2))/(dx)-(d(xy))/(dx)=0#

#rarr color(white)("XX")2y(dy)/(dx)-(y+x(dy)/(dx))=0#

#color(white)("XXXXXXXXXXXX")#(using the Chain and Product rules)

#rarr color(white)("XX")2y(dy)/(dx)-x(dy)/(dx)=y#

#rarr color(white)("XX")(dy)/(dx)(2y-x)=y#

#rarr color(white)("XX")(dy)/(dx)=y/(2y-x)#