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Math Help - Implicit Differentiation

  1. #1
    Junior Member
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    Implicit Differentiation

    I am getting the 0, but its not right. What am I doing wrong??????


    If and , find by implicit differentiation.
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    sqrt(x) +sqrt(y) = 7

    Differentiate both sides with respect to x,

    1/(2sqrt(x)) +[1/(2sqrt(y)](y') = 0
    y' = -[1 / 2sqrt(x)] / [1 / 2sqrt(y)]
    y' = -[1 /sqrt(x)] * [sqrt(y) / 1]
    y' = -sqrt(y) / sqrt(x)
    y' = -sqrt(y/x)

    y(16) = 9
    So, point (16,9)

    y'(16) = -sqrt(9/16) = +,-3/4 ----------------answer.
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