if x^3 + y^3 = 25, find the second derivative

Answer 1

x³ + y³ = 25

3x² + 3y²(dy/dx) = 0

So, dy/dx = -x² / y²

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

= [-2xy² + 2x²y(-x² / y²)] / y⁴

= [-2xy² - 2x⁴y / y²] / y⁴

= [-2xy² - 2x⁴ / y] / y⁴

= (-2xy³ - 2x⁴) / y⁵