Calculus : determine d^2 y/dx^2 when 5x^2 + y^2 = 2?

Question

Determine d^2 y/dx^2 when 5x^2 + y^2 = 2

Anyone have the steps to this one?

Here are the choices
1. 10/y^2
2.- 10/y^3
3. -5/y^3
4.10/y^3
5. -10/y^2

Answer 1

Start with first derivative:

10x+2y dy/dx = 0 ---> dy/dx = - 5x/y

Now take second:

d^y/dx^2 = -5/y +5x/y^2 dy/dx =-5/y +5x/y^2 *(-5x/y)

= -5/y -25x^2/y^3 = -5*(y^2+5x^2)/y^3

Now from starting equation 5x^2 = 2 - y^2

So

d^2y/dx^2 = -5(y^2+2 -y^2)/y^3 =-10/y^3

Number 2 is correct

Answer 2

solve x for 5x^2 + y^2 = 2....x=sqrt((2-y^2)/5)
now find the second derivative (differentiate twice) and there you go.

Answer 3

true