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Math Help - Maclaurin Series

  1. #1
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    Question Maclaurin Series

    Hello, I have a problem that says: Compute the 6th derivative of:
    at x=0.
    So I know that f(x)=\sum_{n=0}^{\infty}(-1)^n\dfrac{\left(\frac{x^2}{4}\right)^{2n+1}}{2n+1  }
    But I'm not sure how to go about and solve it.
    Thanks,
    Matt
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by matt3D View Post
    Hello, I have a problem that says: Compute the 6th derivative of:
    at x=0.
    So I know that f(x)=\sum_{n=0}^{\infty}(-1)^n\dfrac{\left(\frac{x^2}{4}\right)^{2n+1}}{2n+1  }
    But I'm not sure how to go about and solve it.
    Thanks,
    Matt
    Use the fact that the general form of a Maclaurin series is \sum_{n=0}^{\infty}\frac{f^{(n)}(0)x^n}{n!} and compare coefficients to find an equation for the n-th derivative
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  3. #3
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    Hmm, I'm still having some trouble with this problem, could you show me what to do exactly? I know that the maclaurin series is x-x^3/3+x^5/5-...
    So would I compare -(((x^2/4)^3)/2) to ?
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