Implicit Differentiation

Question

If -3y = -3 + 2xy then find d^2y/dx^2 at the point (-1,3) in the simplest form

Answer 1

Take the implicit derivative: -3y' = 2y +2xy' y' = -2y/(3+2x) (note y = 3/(3+2x)) so y' = -6/(3+2x)² which we can get by taking the regular derivative of y(x))

y'' = ((3+2x)(-2y')-(-2y)(2))/(3+2x)²

So simplify by plugging in y and y'