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Math Help - using maclaurin series that we already know

  1. #1
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    using maclaurin series that we already know

    so, i have two really similar questions here:

    1) using the maclaurin series for e^x, show that (e^x)' = e^x

    and 2) using the maclaurin series for sin(x), show that (sin(x))'= cos(x)

    i know what these are, but, i have no idea how to show what they're asking

    any help would be greatly appreciated!
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  2. #2
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    Quote Originally Posted by buttonbear View Post
    so, i have two really similar questions here:

    1) using the maclaurin series for e^x, show that (e^x)' = e^x

    and 2) using the maclaurin series for sin(x), show that (sin(x))'= cos(x)

    i know what these are, but, i have no idea how to show what they're asking

    any help would be greatly appreciated!
    e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + ... + \frac{x^n}{n!} + ...

    take the derivative of both sides ... what do you see?

    now do the same for the maclaurin series for \sin{x}
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  3. #3
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    wait.. how do you take the derivative of factorial?
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  4. #4
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    Quote Originally Posted by buttonbear View Post
    wait.. how do you take the derivative of factorial?
    you don't ... it's a constant multiple of a term of the function.

    for example, the derivative of \frac{x^3}{3!} is \frac{3x^2}{3!} = \frac{x^2}{2!}
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  5. #5
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    oh..obviously
    forgive me, i'm sleep deprived (among other things)
    thank you!
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