Implicit Differentiation - 2nd derivative

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Homework Help Overview

The problem involves finding the second derivative of a function defined implicitly by the equation xy + y² = 1. The original poster attempts to differentiate this equation to find d²y/dx² and expresses confusion over the simplification process leading to the expected answer.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the process of implicit differentiation and the simplification of the second derivative. There is uncertainty regarding the correctness of the answer sheet and the simplification steps involved.

Discussion Status

Some participants express doubt about the accuracy of the answer sheet, while others reconsider their simplification process. There is a recognition that both the original poster's and the answer sheet's results may be valid under different interpretations of simplification.

Contextual Notes

Participants note that the problem originates from a previous test, and there is a suggestion that the instructor should have clarified any discrepancies in the answers provided.

htoor9
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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!
 
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I get your same answer. Perhaps your answer sheet is incorrect?
 
Maybe...I don't know this is from a previous test. I feel like she should've fixed this by now?
 
htoor9 said:
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 :redface:
 

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