Find the value of d^2 y

Question

If x^3 + y^3 = 16, find the value of d^2 y / dx^2 at the point (2, 2)

Answer 1

x³ + y³ = 16

3x² + 3y²(dy/dx) = 0

So, dy/dx = -x² / y²

d²y / dx² = [y²(-2x) + x²(2y)(dy/dx)] / y⁴

=[-2xy² + 2x²y(-x²/y²)] / y⁴

At the point (2,2), d²y / dx² = [-16 + 16(-1)] / 16 = -2