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Math Help - Implicit differentiation

  1. #1
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    Smile Implicit differentiation

    Hello people,

    This question just doesnt help me at all!

    4x^4 + 8xy - 16y = 14

    using implicit differentiation,

    I had (y+2x^2) / (x-2)

    but the answer was different!!!

    Help me out please with steps and explain.

    Thank you so much!!!!!!
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  2. #2
    MHF Contributor chisigma's Avatar
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    If a function is defined in implicit form...

    f(x,y)=0 (1)

    ... then is...

     y^{'} = -\frac{f_{x}^{'} (x,y)}{f_{y}^{'} (x,y)} (2)

    In your case is...

    f(x,y)= 4x^{4} + 8xy -16y -14

    f_{x}^{'} (x,y) = 16x^{3} + 8y

    f_{y}^{'} (x,y) = 8x - 16 (3)

    ... so that...

    y^{'} = - \frac{2x^{3} + y}{x-2} (4)

    Kind regards

    \chi \sigma
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  3. #3
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    Quote Originally Posted by chisigma View Post
    If a function is defined in implicit form...

    f(x,y)=0 (1)

    ... then is...

     y^{'} = -\frac{f_{x}^{'} (x,y)}{f_{y}^{'} (x,y)} (2)

    In your case is...

    f(x,y)= 4x^{4} + 8xy -16y -14

    f_{x}^{'} (x,y) = 16x^{3} + 8y

    f_{y}^{'} (x,y) = 8x - 16 (3)

    ... so that...

    y^{'} = - \frac{2x^{3} + y}{x-2} (4)

    Kind regards

    \chi \sigma
    I completely understand that until you get to step (4)

    Wait I get it, your reducing with 8. I thought you weren't allowed to do that though.
    Last edited by Zanderist; March 14th 2010 at 08:52 PM.
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