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Math Help - Implict functions

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    Implict functions

    When doing these I am unsure of where to place dy/dx

    for example of this problem


    x^2+xy-y^3=xy^2
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  2. #2
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    Quote Originally Posted by sk8erboyla2004 View Post
    When doing these I am unsure of where to place dy/dx

    for example of this problem


    x^2+xy-y^3=xy^2

    If you are using implicit differentiation, take the derivative with respect to x of both sides. When you come across something with a y, use the chain rule.

    You should end up with something that has \frac{dy}{dx} in it, and then make \frac{dy}{dx} the subject.

    Using your example...


    \frac{d}{dx}(x^2 + xy - y^3) = \frac{d}{dx}(xy^2)

    \frac{d}{dx}(x^2) + \frac{d}{dx}(xy) - \frac{d}{dx}(y^3) = \frac{d}{dx}(xy^2)

    2x + x\frac{dy}{dx} + y - 3y^2\frac{dy}{dx} = y^2 + 2xy\frac{dy}{dx}

    Now just make \frac{dy}{dx} the subject.
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