We first find #d/dx# of each term.
#d/dx[xy^2]-d/dx[(1-xy)^2]=d/dx[C]#
#d/dx[x]y^2+d/dx[y^2]x-2(1-xy)d/dx[1-xy]=0#
#y^2+d/dx[y^2]x-2(1-xy)(d/dx[1]-d/dx[xy])=0#
#y^2+d/dx[y^2]x-2(1-xy)(-d/dx[x]y+d/dx[y]x)=0#
#y^2+d/dx[y^2]x-2(1-xy)(-y+d/dx[y]x)=0#
The chain rule tells us:
#d/dx=d/dy*dy/dx#
#y^2+dy/dx d/dy[y^2]x-2(1-xy)(-y+dy/dxd/dy[y]x)=0#
#y^2+dy/dx 2yx-2(1-xy)(-y+dy/dx x)=0#
#dy/dx 2yx-2(1-x)dy/dx x=-y^2-2y(1-xy)#
#dy/dx( 2yx-2x(1-x))=-y^2-2y(1-xy)#x
#dy/dx=-(y^2+2y(1-xy))/(2yx-2x(1-x))#
For #(1,-1)#
#dy/dx=-((-1)^2+2(-1)(1-1(-1)))/(2(1)(-1)-2(1)(1-1))=-1.5#
