find dy/dx by implicit differentiation

Question

1. cos(xy) = 1/(x+y)

Answer 1

dy/dx = { ysin(xy) - 1/(x+y)² }/{ (1/(x+y)² - xsin(xy)) }

Answer 2

cos(xy) = (x+y)^-1

-sin(xy)[y + xy') = -(x+y)^-2(1+y')

-ysin(xy) - xy'sin(xy) = -(x+y)^-2 - y'(x+y)^-2

y'(x+y)^-2 - xy'sin(xy) = ysin(xy) - (x+y)^-2

y'[(x+y)^-2 - xsin(xy)] = ysin(xy) - (x+y)^-2

y' = [ysin(xy) - (x+y)^-2] / [(x+y)^-2 -xsin(xy)]

y' = [ysin(xy)(x+y)² - 1] / [1 - xsin(xy)(x+y)²]