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I don't see that as particularly hard to differentiate.  It is basically a= b(1- cxy)^2+ cx^2.  The derivative is given by 0= 2b(1- xy)(-xy'- y)+ 2cx. Solving for y', -xy'- y= -cx/(b(1-xy)), xy'= cx/(b(1- xy)- y, y'= c/(b(1- xy))- y/x.

That will be 0 when c/(b(1- xy)= y/x, cx= by(1- xy)).

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