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Math Help - Implicit Differentiation, finding slope

  1. #1
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    Implicit Differentiation, finding slope

    Having trouble with this problem, cant seem to get the right answer:

    Use implicit differentiation to find the slope of the tangent line to the curve:

    Implicit Differentiation, finding slope-0bb1403fe8cc171ae0ce71131187d31.png

    at the point (-1,3)

    Ive tried doing it many times and cannot get the right answer for the slope. Any help would be great!
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Hm...

    -x^2 + 2xy + 3y^3 = 74

    2x + 2\left(x\ \dfrac{dy}{dx} + y\right) + 9y^2\ \dfrac{dy}{dx} = 0

    Did you get this? Can you complete it now?
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  3. #3
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    Sort of, I tried working it out and still cant come up with the answer
    The answer is -0.1012658 but I cant work out all the steps properly to show how to get it
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  4. #4
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    Quote Originally Posted by Hockey_Guy14 View Post
    Sort of, I tried working it out and still cant come up with the answer
    The answer is -0.1012658 but I cant work out all the steps properly to show how to get it
    Was that a negative sign or simply a "dash" in front of the formula? Unknown008 assumed it was a "dash" and ignored it in the derivative.

    You say you have "tried doing it many times". Please show us at least one of those tries and perhaps we can see where you are going wrong.
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  5. #5
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    It is a negative in front of the first term, and i got to where unknown008 asked if i got to, but what do i do with the dy/dx parts, that mean i have to differentiate further?
    would it be something like -2x + 2y + 9y^2 = 0? Then separate terms to both sides of the equation to get 2y + 9y^2 = 2x and try to solve? Im confused on where to go after the line Unknown008 provided me.
    Last edited by Hockey_Guy14; January 31st 2011 at 07:32 AM.
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  6. #6
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    I managed to figured out all of the steps and get the right answer, thanks you Unknown008 and HallsofIvy for your help!
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  7. #7
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    Quote Originally Posted by Hockey_Guy14 View Post
    It is a negative in front of the first term, and i got to where unknown008 asked if i got to, but what do i do with the dy/dx parts, that mean i have to differentiate further?
    No, it means solve for dy/dx just as if it were an algebraic unknown.
    would it be something like -2x + 2y + 9y^2 = 0? Then separate terms to both sides of the equation to get 2y + 9y^2 = 2x and try to solve? Im confused on where to go after the line Unknown008 provided me.[/QUOTE]

    You got it? Excellent!
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