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Math Help - The Implicit Function Rule

  1. #1
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    The Implicit Function Rule

    Using the eqn: f(qi,Q-i)= P(qi+Q-i) - c + qiP'Q(qi+Q-i)=0

    and the implicit fn rule: dQ-i/dqi = -df/dqi / df/dQ-i

    = 2P'(Q) + qiP''(Q)/ P'(Q)+qiP''(Q)

    why is it 2P'(Q) on the numerator and only P'(Q) on the denominator?? Any explanation would be greatly appreciated
    Last edited by AEJD99; April 19th 2013 at 02:17 AM.
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  2. #2
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    Re: The Implicit Function Rule

    Hey AEJD99.

    Did you try using implicit differentiation and collecting the terms together?
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  3. #3
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    Re: The Implicit Function Rule

    I think that's what I did but I ended up with P'(Q) + qiP''(Q)/ P'(Q)+qiP''(Q) and couldn't gather where the 2 had come from?

    Thanks for the reply.
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  4. #4
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    Re: The Implicit Function Rule

    Maybe if you can show us your step by step work, we can get a better sense of what you did.
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  5. #5
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    Re: The Implicit Function Rule

    managed to solve it, I hadn't used the chain rule properly as part of the partial differentiation
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