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Math Help - Question about a rule for implicit differentiation

  1. #1
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    Question about a rule for implicit differentiation

    So, I'm given the equation:
    (x^2+y^2)^2 = 4x^2y
    The right side of the equation is easy enough, it requires the chain rule, so it becomes:
    2(x^2+y^2)(2x+2y) right?
    Now, the left side of the equation. My textbook lists it as 4x^2(dy/dx)+8xy.

    My question is, is there some kind of rule for what's happening there, because I don't really understand? At first I tried to apply the product rule, but I guess that was wrong. If someone could clear up what exactly is happening there, that would be great!
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  2. #2
    Newbie hungthinh92's Avatar
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    The problem: (it took me few minutes to understand your problem)
    4x^2y
    the derivative will be solved by using the product rule:
    4*2x*y (derivative\ of\ x)+4x^2\frac{dy}{dx} (derivative\ of\ y,\ so\ you\ have\ to\ write\ down\ \frac{dy}{dx})
    Thus, the result will be: 8xy+4x^2\frac{dy}{dx}
    Last edited by CaptainBlack; June 19th 2010 at 12:11 AM.
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  3. #3
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    So, it IS the product rule. Well, I have no idea what I was doing haha. Thanks so much!
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Ohoneo View Post
    So, I'm given the equation:
    (x^2+y^2)^2 = 4x^2y
    The right side of the equation is easy enough, it requires the chain rule, so it becomes:
    2(x^2+y^2)(2x+2y) right?
    Now, the left side of the equation. My textbook lists it as 4x^2(dy/dx)+8xy.

    My question is, is there some kind of rule for what's happening there, because I don't really understand? At first I tried to apply the product rule, but I guess that was wrong. If someone could clear up what exactly is happening there, that would be great!
    1. Learn the difference between your right and left.

    2. Using the product rule: \frac{d}{dx}(4x^2y)=4 \left( \frac{d(x^2)}{dx}y+x^2\frac{dy}{dx} \right)

    CB
    Last edited by CaptainBlack; June 19th 2010 at 12:12 AM.
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