Find y'' by implicit differentiation.

Question

5x2 + y2 = 3
y'' =?

Answer 1

that would be 5x^2 + y^2 = 3

for y' or dy/dx
10x + 2y y' = 0
y' = -10x/2y = -5x/y
for y''
y'' = (y(-5) - 5x y')/y^2
= (-5y - 5x(-5x/y)/y^2
= -5(y - 5x^2/y)/y^2
= -5(y^2 - 5x^2)/y^3