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Math Help - differential problem

  1. #1
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    differential problem

    Differentiate the equation with respect to the variable and express in terms of . (Use D for ).
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  2. #2
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    Well, do it.

    The first term: \frac{d}{dt}x^{4}\;=\;4\cdot x^{3} \cdot \frac{dx}{dt}

    You do the second term. You'll need the product rule.
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  3. #3
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    Quote Originally Posted by tbenne3 View Post
    Differentiate the equation with respect to the variable and express in terms of . (Use D for ).
    x^4 + 3xy^2 = 8

    \frac{d}{dt}(x^4 + 3xy^2) = \frac{d}{dt}(8)

    \frac{d}{dt}(x^4) + \frac{d}{dt}(3xy^2) = 0

    \frac{d}{dx}(x^4)\,\frac{dx}{dt} + 3x\,\frac{d}{dt}(y^2) + y^2\,\frac{d}{dt}(3x) = 0

    4x^3\,\frac{dx}{dt} + 3x\,\frac{d}{dy}(y^2)\,\frac{dy}{dt} + y^2\,\frac{d}{dx}(3x)\,\frac{dx}{dt} = 0

    4x^3\,\frac{dx}{dt} + 6xy\,\frac{dy}{dt} + 3y^2\,\frac{dx}{dt} = 0

    (4x^3 + 3y^2)\,\frac{dx}{dt} + 6xy\,\frac{dy}{dt} = 0

    6xy\,\frac{dy}{dt} = -(4x^3 + 3y^2)\,\frac{dx}{dt}

    \frac{dy}{dt} = -\left(\frac{4x^3 + 3y^2}{6xy}\right)\frac{dx}{dt}.
    Last edited by Prove It; February 22nd 2010 at 08:28 PM.
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  4. #4
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    Whoops, a little off on the first term. Very clean, though.
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  5. #5
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    Quote Originally Posted by TKHunny View Post
    Whoops, a little off on the first term. Very clean, though.
    Edited. Thanks.
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  6. #6
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    says it is incorrect :\
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    Quote Originally Posted by tbenne3 View Post
    says it is incorrect :\
    Check the edited version...
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  8. #8
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    this is what i entered and it says incorrect: -((4x^3+3y^2)/(6xy))
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  9. #9
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    Quote Originally Posted by tbenne3 View Post
    this is what i entered and it says incorrect: -((4x^3+3y^2)/(6xy))
    That's because it's -\left(\frac{4x^3 + 3y^2}{6xy}\right)D.


    If it's still wrong, go through my working and find my mistake - I've provided you a full solution so it shouldn't be too hard to check it's correct.
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  10. #10
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    That's what "very clean" is all about. You can follow it and see where you may have wandered off. You can also gain great confidence that you have not wandered off. Sloppy can't do that.
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