Implicit Differentiation - 2nd derivative

[htoor9]

Homework Statement

Find d2y/dx2 in terms of x and y for the following equation: xy + y^2 = 1 COMPLETELY SIMPLIFY

Homework Equations

dy/dx

The Attempt at a Solution

so i get -y/(x+2y) for the dy/dx. When I try to find the 2nd derivative and plug in dy/dx, I get 2y(x+y)/(x+2y)^3...the sheet says the correct answer is 2/(x+2y)^3. I don't understand I've done this problem 3 times and still don't get that answer!

 

[rock.freak667]

I get your same answer. Perhaps your answer sheet is incorrect?

 

[htoor9]

Maybe...I don't know this is from a previous test. I feel like she should've fixed this by now?

 

[rock.freak667]

Maybe...I don't know this is from a previous test. I feel like she should've fixed this by now?

Oh my I am sorry I misled you like that. The answer is correct. Well both really. We just didn't simplify it enough!

y''=2y(x+y)/(x+2y)³ = 2(xy+y²)/(x+2y)³

But remember our starting equation? xy+y²= 1