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Math Help - Implicit Differentiation

  1. #1
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    Implicit Differentiation

    I'm having trouble with this question.

    Find dy/dx by implicit differentiation.

    (x+y)/(x-y) = 3x

    First I use the quotient rule getting:

    [(1 + y')(x-y) - (1 - y')(x+y)] / [(x-y)^2] = 3

    Then I factor out y' and solve the equation for y' which gives me:

    y' = [3x^2 - 6xy +3y^2]/[2x - 2y]

    but the answer is:

    [6x - 3y - 1]/[3x + 1]

    not sure what i'm doing wrong so any help would be appreciated. thanks
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  2. #2
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    Don't use the quotient rule.

    Rewrite the equation as

    x+y = 3x(x-y)

    x + y = 3x^2 - 3xy

    and then use implicit differentiation.
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  3. #3
    Super Member bigwave's Avatar
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    Quote Originally Posted by icemanfan View Post
    Don't use the quotient rule.

    Rewrite the equation as

    x+y = 3x(x-y)

    x + y = 3x^2 - 3xy

    and then use implicit differentiation.
    just to add to this:

    1 + y' = 6x - 3y - 3xy'

    y' + 3xy' = 6x - 3y -1

    y'(1 + 3x) = 6x - 3y - 1

    y' = (6x-3y-1)\(3x+1)
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  4. #4
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    oh ok thanks.
    so should I always rewrite such equations first before using implicit differentiation?
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  5. #5
    Super Member bigwave's Avatar
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    Quote Originally Posted by abstraktz View Post
    oh ok thanks.
    so should I always rewrite such equations first before using implicit differentiation?
    no, you don't have to

    but as icemanfan suggests

    rewriting is just a modification to make the next steps more simple.

    not all implicit differentiation would need rewriting.
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