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Math Help - Product rule in terms of implicit differentiation

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    Product rule in terms of implicit differentiation

    1) x^2 + xy - y^2 = 4
    x^2 + x*y(x) - y(x)^2 = 4

    I understand this much: 2x + ____ + 2y*(dy/dx) = 0
    But I don't understand how to differentiate the middle portion properly. I'm assuming it's just the product rule, but doing it didn't lead me to the right answer.

    2) x^4(x + y) = y^2(3x - y)

    Product rule again?
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  2. #2
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    Quote Originally Posted by CFem View Post
    1) x^2 + xy - y^2 = 4
    x^2 + x*y(x) - y(x)^2 = 4

    I understand this much: 2x + ____ + 2y*(dy/dx) = 0
    But I don't understand how to differentiate the middle portion properly. I'm assuming it's just the product rule, but doing it didn't lead me to the right answer.
    u = x \: \rightarrow \: u' = 1

    v = y \: \rightarrow \: v' = \frac{dy}{dx}

    \frac{dy}{dx} = u'v + v'u = y + x\frac{dy}{dx}

    Isolate the dy/dx terms and solve for dy/dx
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