Question

Find the second derivative of xy +y^2 = 1.
The first derivative is -y(x + 2y)^(-1).

Answer 1

Dx(xy +y^2 = 1)
Dx(xy) +Dx(y^2) = Dx(1)
(x'y + xy') +(2y y') = (0)
x'y + y'(x +2y) = 0
y'(x +2y) = -x'y
y' = -x'y/(x +2y)