# Taylor series

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• Nov 26th 2006, 05:59 PM
@_@
d) Determine the Taylor series of f'(x) around x=0. Can you do so without using b)?

isn't it the same thing as b), just without the first term i guess?? or no?
• Nov 26th 2006, 06:02 PM
ThePerfectHacker
Quote:

Originally Posted by @_@
d) Determine the Taylor series of f'(x) around x=0. Can you do so without using b)?

isn't it the same thing as b), just without the first term i guess?? or no?

You have,
$\displaystyle f(x)=\ln (1-x)$

And that,
$\displaystyle f'(x)=-\frac{1}{1-x}$
But this is a geometric series that you should recognize,
$\displaystyle -1+x-x^2+x^3-... = \sum_{k=0}^{\infty} (-1)^{k+1}x^k$
• Nov 26th 2006, 06:44 PM
@_@
how is it related to part b then?
• Nov 26th 2006, 06:57 PM
ThePerfectHacker
Quote:

Originally Posted by @_@
how is it related to part b then?

Ah if you differenciate,
$\displaystyle -x+\frac{x^2}{2}-\frac{x^3}{3}+\frac{x^4}{4}-...$
Term by term,
$\displaystyle -1+x-x^2+x^3-...$

(NOTE: I made a mistake in my other post about the geometric series. It is corrected now).
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