How do i differentiate x^2 + 2xy + y^2 = 1?

so far I have
2x + 2xy +2xy' + 2yy' = 0
2x + 2y +2xy' +2yy' = 0
but i don't know what to do from here

1 answer

not quite
2x + 2y + 2xy' + 2yy' = 0
(x+y)y' = -(x+y)
y' = -(x+y)/(x+y) = -1
huh? seems weird, until you realize that you started with
(x+y)^2 = 1
x+y = ±1
y = ±1-x
so y' = -1
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