(y/x)'/[ 1+(y/x)? ]=? (x? +y? )'/(x? +y? )
[(y' x-y)/x? ]/[ 1+(y/x)? ]=? (2x+2y y')/(x? +y? )
Y is a function of x, and the derivative should use the derivative rule of compound function.
(y' x-y)/(x? +y? )=(x+y y')/(x? +y? )?
y' x-y=x+y y'→y'(x-y)=x+y
y'=(x+y)/(x-y)