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Math Help - Implicit differentiation.

  1. #1
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    Implicit differentiation.

    Can you help with one more?
    X^2+2xy+y^2=15
    2x+2x(dy/dx)+2y+2y(dy/dx)=0
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  2. #2
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    Alright... I'm not convinced I've got this right as I'm quite new to implicit differentiation myself... but here's what I got step by step (do not take this as correct though).

    \frac{d}{dx}(x^2) + \frac{d}{dx}(2xy) + \frac{d}{dx}(y^2) = \frac{d}{dx}(15)

    2x + 2y + 2x + \frac{dy}{dx}\frac{d}{dy}(y^2) = 0

    2x + 2y + 2x + \frac{dy}{dx}2y = 0

    \frac{dy}{dx} = \frac{4x + 2y}{2y} = \frac{2x + y}{y}

    like I said, check it first, I'm havent convinced myself...
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  3. #3
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    Quote Originally Posted by isp_of_doom View Post
    Alright... I'm not convinced I've got this right as I'm quite new to implicit differentiation myself... but here's what I got step by step (do not take this as correct though).

    \frac{d}{dx}(x^2) + \frac{d}{dx}(2xy) + \frac{d}{dx}(y^2) = \frac{d}{dx}(15)

    2x + 2y + 2x {\color{red}\frac{dy}{dx}} + \frac{dy}{dx}\frac{d}{dy}(y^2) = 0

    2x + 2y + 2x {\color{red}\frac{dy}{dx}} + \frac{dy}{dx}2y = 0

    [snip]
    Corrections in red.

    But the question becomes trivial if it's observed that the left hand side is (x + y)^2 and therefore the equation can be written x + y = \pm \sqrt{15}.
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  4. #4
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    Sorry Mr. Fantastic, but won't the 2xy alter that =\pm\sqrt{15}
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  5. #5
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    Quote Originally Posted by isp_of_doom View Post
    Sorry Mr. Fantastic, but won't the 2xy alter that =\pm\sqrt{15}
    x^2 + 2xy + y^2 = 15 \Rightarrow (x + y)^2 = 15 \Rightarrow ....
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  6. #6
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    so the answer is 1?
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  7. #7
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    Quote Originally Posted by Nightasylum View Post
    so the answer is 1?
    No. Try again and be more careful.
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