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Homework Help: 15th derivative of a binomial/maclaurin series

  1. Apr 26, 2010 #1
    1. The problem statement, all variables and given/known data

    sqrt(1+x^4)

    use the binomial series to find the maclaurin series for the above function. then use that to find the 15th derivative at 0.


    2. Relevant equations

    -binomial series


    3. The attempt at a solution

    I've gotten to:

    [tex]\Sigma[/tex] (k n) (x^(4n))
    from n=0 to infinity

    How can i use this to find derivatives?
     
  2. jcsd
  3. Apr 26, 2010 #2

    lanedance

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    i haven't checked what you've got to...

    but if you write out the form for a maclaurin series in terms of its dereivatives, fror ecach term, notice the power of x & the order derivative in the coefficient are always the same
     
  4. Apr 26, 2010 #3

    lanedance

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    [tex] f(x) = f(0) + \frac{f'(0)}{1!}x+\frac{f^''(0)}{2!}x^2+..+\frac{f^{n}(0)}{n!}x^n+.. [/tex]

    [tex] f(x) = f(0) + \frac{f^{1}(0)}{1!}x^1+\frac{f^{2}(0)}{2!}x^2+..+\frac{f^{n}(0)}{n!}x^n+.. [/tex]
     
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