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Math Help - Implicit differentiation

  1. #1
    iceycool
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    Question Implicit differentiation

    Find dy/dx by implicit differentiation given that y satisfies the following equation:

    7*x^3-8*x^2*y-2*x*y^2=8, i.e., .

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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by iceycool View Post
    Find dy/dx by implicit differentiation given that y satisfies the following equation:

    7*x^3-8*x^2*y-2*x*y^2=8, i.e., .

    Differentiating we get

    d/dx[7*x^3-8*x^2*y-2*x*y^2]=0,

    then:

    d/dx[7*x^3] - d/dx[8*x^2*y] - d/dx[2*x*y^2]=0,

    simplifying the derivative in the first term:

    [21*x^2] - d/dx[8*x^2*y] - d/dx[2*x*y^2]=0

    Now the second term:

    [21*x^2] - [16*x*y+8*x^2 * dy/dx] - d/dx[2*x*y^2]=0

    Now the third term:

    [21*x^2] - [16*x*y+8*x^2 * dy/dx] - [2*y^2+4*x*y * dy/dx]=0

    Now simplify to:

    dy/dx = [21*x^2 - 16*x*y - 2*y^2]/[8*x^2 + 4*x*y]

    RonL

    (please check this carefully)
    Checked by PerfectHacker and confiremd.
    Last edited by ThePerfectHacker; October 4th 2006 at 01:14 PM.
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