Answer to Question #95397 in Calculus for Umar

Question

Find Y' given x + xy + y = 2

Answer 1

$x+xy+y=2\\ y={\frac {(2-x)} {(x+1)}}\\ y'=({\frac {(2-x)} {(x+1)}})'={\frac {(2-x)'*(x+1)-(2-x)*(x+1)'}{(x+1)^2}}=\\ ={\frac {(-1)*(x+1)-(2-x)*1}{(x+1)^2}}={\frac{-3}{(x+1)^2}}$

answer: ${\frac{-3}{(x+1)^2}}$