(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If [tex]\sum_{n=0}^{\infty} a_{n}x^n[/tex] is a Taylor series that converges to f(x) for all real x, then f'(1) = ?

2. Relevant equations

A Taylor series:

[tex]\sum_{n=0}^{\infty} \frac {f^{(n)}(c)}{n!}(x-c)^n[/tex]

and the dirv of a Taylor series:

[tex]f'(x)=\sum_{n=0}^{\infty} na_{n}(x-c)^{n-1}[/tex]

3. The attempt at a solution

I started by taking the derivative of the basic Taylor serie:

[tex]f'(x)=\sum_{n=0}^{\infty} na_{n}(x-c)^{n-1}[/tex]

Then simply plugging in 1. I guess I was just thinking this is might be centered at 0, so I put in 0 for c, although the problem doesn't specify.

I end up with the expression:

[tex]f'(1)=\sum_{n=0}^{\infty}n\frac {f^{(n)}(0)}{n!}[/tex]

At this point I'm not sure what to do because I don't know the function f(x). It seems like the answer should be numerical, but the question is quite vague. Maybe this is blatantly simple and I'm just failing to see it, but any tips would be appreciated.

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# Homework Help: Derivative of a Taylor Series f(x) is unknown

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