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Math Help - Nth Derivative Induction Proof

  1. #1
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    Nth Derivative Induction Proof

    Hey
    I have this problem on proof by induction that I'm struggling to do.

    The problem is to prove the nth derivative of  f(x)= \frac{1}{\sqrt{1-4x}}

    I have worked out that the nth derivative is  f^{(n)}(x) = \frac{(2n)!}{n!} \frac{1}{(1-4x)^{n+\frac{1}{2}}}


    But I'm not sure how to go about completing this. My lecturer only covered induction briefly and my textbook doesn't cover it either... Also I have only done basic sequence proofs so any help would be much appreciated.
    Last edited by mr fantastic; September 27th 2009 at 01:29 AM. Reason: Fixed the latex
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  2. #2
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    Another way to represent it is:

    \frac{d^{n}x}{dx^{n}}\left(\frac{1}{\sqrt{1-4x}}\right)=\frac{{\Pi}_{k=1}^{n}(2(2k-1))}{(1-4x)^{\frac{2n+1}{2}}}

    But yours looks good.
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  3. #3
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    I already have a way of representing it what I need help with is the induction proof of <br />
f^{(n)}(x) = \frac{(2n)!}{n!} \frac{1}{(1-4x)^{n+\frac{1}{2}}}
    Last edited by mr fantastic; September 27th 2009 at 01:30 AM. Reason: Re-wrote using latex
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  4. #4
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    I have attached a solution.

    Didn't realize how the latex editor on here worked before I had written it all and I am to lazy to change it to be suitable for the forum.
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