Find y'' by implicit differentiation. x^2 + 2y^2 = 2

Answer 1

We differentiate implicitly given equation: 2x + 2yy' = 0, so y' = - x/y; then y'' = - (y - y'x)/y^2.

^{We substitude here y' = -x/y: y'' = - (y + x^2/y)/y^2 = - (y^2 + x^2)/y^3 = - 2/y^3}