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Math Help - implicit diff. question

  1. #1
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    implicit diff. question

    (x+y)^3 = x^3 + y^3 at the point (-1,1). We need to find y' ... what do?

    Here's what I did, please tell me where I went wrong.

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

    How do I proceed?
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  2. #2
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    3(x+y)^2 (1+y') = 3x^2 + 3y^2 y'
    3(x^2 + 2xy + y^2) (1+y') = 3x^2 + 3y^2 y'

    Keep solving and then you want to isolate the y' in one side and the x and y in the other. Then you'll solve for y'.
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  3. #3
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    Quote Originally Posted by Arturo_026 View Post
    3(x+y)^2 (1+y') = 3x^2 + 3y^2 y'
    3(x^2 + 2xy + y^2) (1+y') = 3x^2 + 3y^2 y'

    Keep solving and then you want to isolate the y' in one side and the x and y in the other. Then you'll solve for y'.
    I got as far as 6xy+3y^2 = 3y^2 y' / 1+ y'. How do I proceed from there?
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  4. #4
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    Hold on, This is wrong. give me a bit more time to correct it
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  5. #5
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    Look, buddy. How did you go from

    3(x^2 + 2xy + y^2) (1+y') = 3x^2 + 3y^2 y'<br />

    to

    3[x^2 + 2xy + y^2 + y'(x^2 + 2xy + y^2)] = 3x^2 + 3y^2 y'<br />

    ???



    EDIT: Nevermind, I'll wait until your edit.
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  6. #6
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    (x^2 + 2xy + y^2)(1 + y') = x^2 + y^2 y'
    x^2 + 2xy + y^2 + x^2 y' + 2xy y' + y^2 y' = x^2 + y^2 y'
    y' (x^2 + 2xy) = -2xy - y^2
    y' = (-2xy - y^2)/(x^2 + 2xy)

    This should be correct.
    I apologize for my mistake, if it serves as an excuse, I was solving it in my head because i couldn't find paper.
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  7. #7
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    The problem I was having is that I didn't expand ASAP. Your step by step solution helped me see my mistakes. Thanks for the help, bromosapien. And no worries about the error.
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