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Math Help - Proof of double derivative.

  1. #1
    Junior Member cupid's Avatar
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    Proof of double derivative.

    Question - In Pic


    My progress is that i found out that f''(x) = \frac{[f'(x)]^2}{f(x)}

    but i couldn't get to the solution
    Attached Thumbnails Attached Thumbnails Proof of double derivative.-12.png  
    Last edited by mr fantastic; February 28th 2011 at 11:01 AM. Reason: Re-titled.
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  2. #2
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    If you use the identity:

    \cos{x} + i\sin{x} = e^{ix},

    then

    y = e^{ix} \cdot e^{3ix} \cdot ... \cdot e^{\left(2n-1\right)ix}

    = e^{ix + 3ix + ... + \left(2n-1\right)ix}

    = e^{ix\left(1 + 3 + ... + 2n-1\right)

    = e^{n^2ix}
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  3. #3
    Junior Member cupid's Avatar
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    Thanks a lot Andrew
    that made the question soo simple
    thanks a lot
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