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Math Help - Help with partial deratives

  1. #1
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    Help with partial deratives

    I have to show that u_{xx} = u_{t}

    for u(x,t) = \frac{1}{\sqrt{4\pi t}} exp(\frac{-x^2}{4t})

    For u_{xx}, I got u_{xx}= \frac{exp(\frac{-x^2}{4t})}{4 \sqrt{\pi} t^\frac{3}{2}} (\frac {x^2}{t} -1})

    and for u_{t}, I got u_{t}= \frac{exp(\frac{-x^2}{4t})}{4 \sqrt{\pi} t^\frac{3}{2}} (\frac {x^2}{2} -\frac{1}{t^2})

    Is either derivative correct? I think I am close but cant quite figure where I am going wrong.

    Help please!
    Last edited by tammyl; March 25th 2013 at 12:11 PM.
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  2. #2
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    Re: Help with partial deratives

    The correct answer is uxx = ut = [exp(-x2/4t)/4sq. root pi *t3/2] * (-1 + x2/2t).

    Basically something is going wrong within the brackets of your answer. Check those.
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  3. #3
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    Re: Help with partial deratives

    If you want to check your intermediate result,

    u_x=-\frac{xe^\frac{-x^2}{4t}}{4 \sqrt{\pi} t^\frac{3}{2}}

    I got the same answer as mrmaaza123 for u_{xx} and u_t.

    - Hollywood
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  4. #4
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    Re: Help with partial deratives

    the two answers above are correct if you are looking for some help on it.. wolfram math have a nice applet to get partial derivatives and also shows the workings.
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  5. #5
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    Re: Help with partial deratives

    Can anyone show me the steps in solving u_{t}?

    I have u_{xx} now - thanks to you all!
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  6. #6
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    Re: Help with partial deratives

    For u_t. Use the product rule to get:

    u_t=\frac{1}{\sqrt{4\pi t}}\frac{x^2}{4t^2}e^{-\frac{x^2}{4t}}-\frac{1}{4\sqrt{\pi}t^{3/2}}e^{-\frac{x^2}{4t}} then factor out an \frac{e^{-\frac{x^2}{4t}}}{4\sqrt{\pi}t^{3/2}} and then your left with the correct u_t Hope this helps. p.s in the first product dont forget that  \sqrt{4\pi t} 4t^2= 8\sqrt \pi t^{5/2}
    Last edited by joeDIT; March 25th 2013 at 03:34 PM.
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