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Thread: Implicit Differentiation #1

  1. August 10th 2009, 11:41 AM #1
    skeske1234
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    Implicit Differentiation #1

    find dy/dx

    (x+y)^2=x^2+y^2

    i keep getting 1 as the answer but the answer in the back says -y/x
    Last edited by mr fantastic; August 12th 2009 at 03:58 PM. Reason: Changed post title
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  2. August 10th 2009, 11:47 AM #2
    earboth
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    Quote Originally Posted by skeske1234 View Post
    find dy/dx

    (x+y)^2=x^2+y^2

    i keep getting 1 as the answer but the answer in the back says -y/x
    Use the chain rule:

    (x+y)^2=x^2+y^2~\implies~2(x+y)(1+y')=2x+2y\cdot y'

    {\color{white}(x+y)^2=x^2+y^2}~\implies~ x+xy'+y+yy'=x+yy'

    {\color{white}(x+y)^2=x^2+y^2}~\implies~ xy'+y=0

    {\color{white}(x+y)^2=x^2+y^2}~\implies~y'=-\dfrac yx
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