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Implicit Differentiation Question - Stuck

  1. Apr 24, 2013 #1
    1. The problem statement, all variables and given/known data

    Use implicit differentiation to find y' given y/(x-y) = x^2+1.


    2. Relevant equations



    3. The attempt at a solution

    Hi, I'm doing an online course for Calculus 12, and I have been struggling with Implicit Differentiation. I am hoping someone could maybe help me. Thanks.

    I'm not positive I'm doing this right, but maybe someone can point me in the right direction. This is what I have so far

    y/(x-y) = x^2+1

    y=(x^2+1)(x-y)

    y' = (2x)(x-y)+(x^2+1)(1-y')

    y' = 2x^2-2xy+x^2-x^2y'+1-y'

    This is where I get stuck and am not sure if I'm making a mistake or know what to do next. Any help would be appreciated, thank you.
     
    Last edited by a moderator: Apr 24, 2013
  2. jcsd
  3. Apr 24, 2013 #2
    y/(x-y) = x^2+1

    y=(x^2+1)(x-y)

    y' = (2x)(x-y)+(x^2+1)(1-y')

    y' = 2x^2-2xy+x^2-x^2y'+1-y'

    2y'+x^2y' = 3x^2-2xy+1

    y'(2+x^2) = 3x^2-2xy+1

    y' = (3x^2-2xy+1)/(2+x^2)

    That's what I got as my continued attempt, does that look right?
     
  4. Apr 24, 2013 #3

    vela

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    Up to here is correct. If you did the subsequent algebra correctly, you should have the right answer.

    In this problem, you can solve the original equation for y. Try that and then differentiate the resulting expression. See if you get the same result.
     
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