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Math Help - help please?

  1. #1
    ilovecalculus
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    help please?

    hey- how do i find a power series for f'(x) if

    f(x)= sum from n=0 to n=infinity [(-1^n)*x^(2n)]/[(2n)!]

    thanks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ilovecalculus
    hey- how do i find a power series for f'(x) if

    f(x)= sum from n=0 to n=infinity [(-1^n)*x^(2n)]/[(2n)!]

    thanks.
    How to find a power series representation of f'(x) if:

    <br />
f(x)=\sum_{n=0}^{\infty} (-1)^n \frac{x^{2n}}{(2n)!}<br />
?

    Differentiate term by term (I know this works for this series so I won't worry
    about convergence).

    <br />
f'(x)=\sum_{n=0}^{\infty} (-1)^n \frac{\frac{d(x^{2n})}{dx}}{(2n)!}<br />
,

    so:

    <br />
f'(x)=\sum_{n=0}^{\infty} (-1)^n \frac{2n\ x^{2n-1}}{(2n)!}<br />
,

    Simplifying slightly:


    <br />
f'(x)=\sum_{n=0}^{\infty} (-1)^n \frac{x^{2n-1}}{(2n-1)!}<br />
.

    RonL
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