Question

use implicit differentiation to find (d^2y)/(dx^2) y^2-x^2=4

Answer 1

How far did you get?

Answer 2

All I know is that dy/dx=x/y.

Answer 3

Let's see: \(2y\cdot y' - 2x = 0\) Yup. I agree.

Here's a plan for the 2nd derivative, rather than starting with the simplified form that you provided, why not use the unsimplified form that I wrote. Is it more obvious how to proceed?

Answer 4

So I would pull the derivative from the unsimplified form?

Answer 5

You can use either. The simplified form will require you to use the Quotient Rule. The unsimplified requires the Product Rule, instead. Are you more comfortable with one or the other?

Answer 6

I would rather use the quotient rule.