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Math Help - Implicit Differentiation issue

  1. #1
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    Implicit Differentiation issue

    I'm not sure if I just hit my limit for the day regarding Calc, but I may have. I was wondering if someone could take a look at this problem for me. I have the solution in front of me, with most of the steps, but I don't see how to go from the last step to the conclusion.

    The problem is stated:
    If x^2-xy+y^2=3, find y' and y".
    2x-xy'-y+2yy'=0

    Implicit Differentiation issue-p91.png


    I just don't see how to go from the
    Implicit Differentiation issue-1.png
    to 18/(x-2y)^3

    Is there something that is incredibly obvious that I am missing, or is it just another problem with this book? (I have found a few errors already)

    Thank you! Any input would be appreciated.
    Attached Thumbnails Attached Thumbnails Implicit Differentiation issue-p91.png  
    Last edited by jman242; July 14th 2013 at 10:37 AM.
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  2. #2
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    Lexington, MA (USA)
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    Re: Implicit Differentiation issue

    Hello, jman242!

    Hope you have a sense of humor.


    \text{Given: }\:x^2-xy+y^2\:=\:3.\quad\text{Find }y'\text{ and }y".

    \text{I just don't see how to go from }\:\frac{6(x^2-xy+y^2)}{(x-2y)^3}\:\text{ to }\:\frac{18}{(x-2y)^3}

    Look at the "Given" . . .

    We were told that:- x^2-xy+y^2 is equal to 3. . . *facepalm*

    Get it?


    Watch for this . . .
    It turns up in many Implicit Differentiaton problems.
    Thanks from topsquark
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  3. #3
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    Re: Implicit Differentiation issue

    I will admit I chuckled over what was my confusion. I always love tutoring someone and making them see their own error and then point out I do the same exact mistakes. Thanks Soroban. I wish you could have seen my face when I understood, I know you would have laughed. Cheers, and to more mathemagical humor in the future...
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