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Math Help - Related Rates

  1. #1
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    Related Rates

    I am having a little difficulty with this problem while using the related rates method. Here is the problem:

    Y^2 + 2XY^2 - 3X +1 = 0

    I know you need to differentiate just as you would with implicit, but you need to insert either (dx/dt) or (dy/dt) with the respective x, y terms. I am confused what to insert for the 2nd term which is using the product rule. I am thinking to pull the 2 in front of the term to multiply, but I don't know whether to put (1) or (dx/dt) for the x term and the same for they y term. Please help!
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  2. #2
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    Quote Originally Posted by kdogg121 View Post
    I am having a little difficulty with this problem while using the related rates method. Here is the problem:

    Y^2 + 2XY^2 - 3X +1 = 0

    I know you need to differentiate just as you would with implicit, but you need to insert either (dx/dt) or (dy/dt) with the respective x, y terms. I am confused what to insert for the 2nd term which is using the product rule. I am thinking to pull the 2 in front of the term to multiply, but I don't know whether to put (1) or (dx/dt) for the x term and the same for they y term. Please help!
    What exactly are you trying to find? Please post the question exactly as it is written in your book.
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  3. #3
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    Well the instructions indicate to find dy/dx by implicit differentiation, however my professor assigned this set of problems twice, he wanted us to do it by implicit as well as the related rates method. I am mostly confused what the 2nd term in the problem would look like differentiated by the method.
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  4. #4
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    If we had XY as part of an equation being differentiated through related rates wouldn't this be:

    X(dy/dt) + Y(dx/dt) ?

    As the X on the outside of the first time is undifferentiated and the Y inside is making it dy/dt , the Y on the second term is undifferentiated while the X inside is differentiated as dx/dt Would this be correct?
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    Quote Originally Posted by kdogg121 View Post
    Well the instructions indicate to find dy/dx by implicit differentiation, however my professor assigned this set of problems twice, he wanted us to do it by implicit as well as the related rates method. I am mostly confused what the 2nd term in the problem would look like differentiated by the method.
    Are you saying that you need to differentiate the given expression with respect to time? Note that from the chain rule \frac{dy}{dt} = \frac{dy}{dx} \, \frac{dx}{dt}, \frac{d y^2}{dt} = \frac{d y^2}{dy} \, \frac{dy}{dt} = 2y \frac{dy}{dt} = 2y \frac{dy}{dx} \, \frac{dx}{dt} etc.

    Please post the exact question and the exact instructions. If you're not clear about those two things, I suggest you first ask your professor for clarification.
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