Termwise Differentiation of Power Seriesby Hootenanny Tags: differentiation, power, series, termwise 

#1
Mar2908, 01:47 PM

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PF Gold
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For those who don't know I'm writing a tutorial (Introduction / Summary of Differentiation) in the tutorials forum. I have come to the point of introducing Transcendental functions. I would like to introduce the exponential function first (via the Taylor series) and then present the natural logarithm as it's inverse. Although not entirely necessary, I would like to present a concise proof of termwise differentiation of power series in the tutorial.
If anyone knows of a concise online proof, or even better, would be willing to contribute a proof directly, please let me know, either in this thread or via PM. Thanks for your time. 



#2
Mar2908, 05:10 PM

P: 28

I would say that it follows from the linearity of differentiation




#3
Mar3008, 06:53 AM

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Thanks
PF Gold
P: 38,881

Because you are talking about an infinite series, you also need the fact that a power series converges uniformly inside its radius of convergence.



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