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  1. #1
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    Implicit differentiation

    suppose (x^2/26)+(y^2/64)=1 and y(1)=7.88811 Find y'(1) by implicit diffentiation

    I get y'=16x/9y but I'm not sure where to go from there to get y'(1)?
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  2. #2
    Super Member Quacky's Avatar
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    Re: Implicit differentiation

    Disagree with your differentiation, firstly.

    \frac{x}{13}+\frac{y}{32}\cdot\frac{dy}{dx}=0

    \frac{x}{13}=-\frac{y}{32}\cdot\frac{dy}{dx}

    \frac{dy}{dx}=\frac{-32x}{13y}

    Anyway, you know that y(1)=7.88811 so substitute that into the original equation to find the value for x at this point. Then it becomes a case of substitution.
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  3. #3
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    Re: Implicit differentiation

    Sorry I typoed
    Should have been
    (x^2/36)+(y^2/64)=1

    Forgive me, but I'm just not making a connection between the information y(1)=7.88811 and the original equation. I know I need to substitue and solve for x, but there's a point in my brain that doesnt want to accept how this should occur.

    is it just plug in 7.88811 for y^2 and solve for x?
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  4. #4
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    Re: Implicit differentiation

    Quote Originally Posted by CyanBC View Post
    Sorry I typoed
    Should have been
    (x^2/36)+(y^2/64)=1

    Forgive me, but I'm just not making a connection between the information y(1)=7.88811 and the original equation. I know I need to substitue and solve for x, but there's a point in my brain that doesnt want to accept how this should occur.

    is it just plug in 7.88811 for y^2 and solve for x?
    \frac{x^2}{36} + \frac{y^2}{64} = 1

    \frac{y^2}{64} = 1 -\frac{x^2}{36}

    y^2 = 64\left(1 -\frac{x^2}{36}\right)

    y = \pm 8\sqrt{1 -\frac{x^2}{36}}

    y(1) = \pm 8\sqrt{1 -\frac{1}{36}} = \pm 8\sqrt{\frac{35}{36}} \approx \pm 7.88811

    they chose to use the positive value of y on the ellipse.

    so, correctly determine dy/dx and sub in 7.88811 for y and 1 for x to get the slope at that point on the ellipse.
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  5. #5
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    Re: Implicit differentiation

    Thank you both very much. That one was driving me crazy. I just need to relax and think a bit more clearly when I get these.

    Solution.
    -16x/9y is -16(1)/9(7.88811) or -0.225374364426685

    Again, thank you very much!
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