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Implicit Differentiation - 2nd derivative

  1. Nov 1, 2010 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations

    dy/dx

    3. 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!
     
  2. jcsd
  3. Nov 1, 2010 #2

    rock.freak667

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    Homework Helper

    I get your same answer. Perhaps your answer sheet is incorrect?
     
  4. Nov 1, 2010 #3
    Maybe...I don't know this is from a previous test. I feel like she should've fixed this by now?
     
  5. Nov 1, 2010 #4

    rock.freak667

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    Homework Helper

    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 :redface:
     
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