Suppose 4y + xy = 2. Evaluate d^2y/dx^2 at the point (-3, 2).

Answer 1

4y + xy = 2
4y' + y + xy' = 0
y' = -y/(x+4)

Now you can use the quotient rule or another implicit differentiation.

4y" + y' + y'^2 + xy" = 0

So, now just plug in (-3,2) to evaluate it there.