Take the derivative, d/dx of both sides
d/dx (-1)=d/dx (x)-d/dx(ycot^2(x-y))
0=1-yd/dx(cot^2(x-y))-(dy)/dx cot^2(x-y)
(dy)/dx cot^2(x-y)+yd/dx(cot^2(x-y))=1
(dy)/dx cot^2(x-y)+y(-2 cot(x - y) csc^2(x - y))(1-dy/dx)=1
(dy)/dx cot^2(x-y)-2ycot(x - y) csc^2(x - y)+2ycot(x - y) csc^2(x - y)dy/dx=1
(dy)/dx cot^2(x-y)+dy/dx2ycot(x - y) csc^2(x - y)-2ycot(x - y) csc^2(x - y)=1
(dy)/dx (cot^2(x-y)+2ycot(x - y) csc^2(x - y))-2ycot(x - y) csc^2(x - y)=1
(dy)/dx (cot^2(x-y)+2ycot(x - y) csc^2(x - y))=1+2ycot(x - y) csc^2(x - y)
(dy)/dx =(1+2ycot(x - y) csc^2(x - y))/(cot^2(x-y)+2ycot(x - y) csc^2(x - y))