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## Homework Statement

Determine y'' when 5x^2 + 3y^2 = 4.

## The Attempt at a Solution

So I found the first derivative using the power rule and chain rule,

10x + 6yy' = 0

Which I then solved for y',

y' = -10x/6y = -5x/3y

Next I found the second derivative using quotient rule,

y'' = (-15y + 15xy')/(3y)^2

This is the part where I am lost, since all the multiple choice answers involve no y' nor is there a x.

I don't know how to get rid of the x and the y' in the equation. Any help will be appreciated as to simplifying the equation even further and as to how.