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    Lightning55's Avatar
    Lightning55 Posts: 97, Reputation: 7
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    #1

    Sep 26, 2009, 04:51 PM
    Implicit Differentiation and Second Derivative
    Okay, I have the first derivative, but I'm not sure.
    This is the original equation



    and so...



    What I don't get is that we have to solve the first derivative at (3,7). Do I just plug in the 7 into dy/dx or did I do something wrong in getting the derivative?

    And for the second derivative, I just got



    Am I doing something wrong or is this right?
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #2

    Sep 27, 2009, 04:26 AM
    The first derivative should be . No negative.

    Now, to find the second derivative, differentiate 1/(y+1):

    Quotient rule:



    But, remember that y'=1/(y+1). Sub that in:



    Also, from what I can tell, the point (3,7) does not lie on the curve, but (7,3) does.

    I think you may have them reversed.

    Therefore, if y=3, then for the first derivative we have 1/(1+3)=1/4
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #3

    Sep 27, 2009, 08:10 AM

    Good catch for the (3,7) coordinate Galactus. However, I didn't see a negative sign in front of the first derivative... :)

    I was answering the question when the second derivative got me confused. Thank you, now I know how to cope with such a derivation :)
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #4

    Sep 27, 2009, 08:55 AM
    However, I didn't see a negative sign in front of the first derivative... :)
    There is none in the first derivative, but there is in the second. Look close at the quotient rule.
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #5

    Sep 27, 2009, 09:11 AM

    Ah, the way you put it... it sounded as if the first derivative was good except for the negative sign..

    Quote Originally Posted by galactus
    The first derivative should be
    Lightning55's Avatar
    Lightning55 Posts: 97, Reputation: 7
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    #6

    Sep 27, 2009, 09:14 AM

    Oh I get it. Somehow when I was using the quotient rule, I got -y instead of -y'

    And no, I did not have a negative function for the first derivative.

    And yes, I may have the points mixed up.

    Thanks.

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