# Math help please? **URL:** \ **Category:** Factual Questions\ **Created:** [November 12, 2015, 3:10pm UTC](https://boards.straightdope.com/t/math-help-please/737374 "2015-11-12T15:10:48Z")\ **Posts on this page:** 13\ **Page:** 1
**Author:** ![brahmsacademic](https://avatars.discourse-cdn.com/v4/letter/b/838e76/32.png) [@brahmsacademic](https://boards.straightdope.com/u/brahmsacademic)\ **Post date:** [November 12, 2015, 3:10pm UTC](https://boards.straightdope.com/t/math-help-please/737374/1 "2015-11-12T15:10:48Z")
How do you prove that the derivative of the sum as k goes from 0 to infinity of f(sub-k)(x) = the sum as k goes from 0 to infinity of the derivative of f(sub-k)(x). Thanks in advance! ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [November 12, 2015, 3:12pm UTC](https://boards.straightdope.com/t/math-help-please/737374/2 "2015-11-12T15:12:19Z")
Have you tried anything so far? This sounds like a homework question. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 12, 2015, 3:49pm UTC](https://boards.straightdope.com/t/math-help-please/737374/3 "2015-11-12T15:49:06Z")
Any proof is going to depend on your axioms. What axioms are you using about limits and sums? ---
**Author:** ![ElderSign](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eldersign/32/8263_2.png) [@ElderSign](https://boards.straightdope.com/u/ElderSign)\ **Post date:** [November 12, 2015, 4:36pm UTC](https://boards.straightdope.com/t/math-help-please/737374/4 "2015-11-12T16:36:37Z")
Same question asked last night: [Yahoo | Mail, Weather, Search, Politics, News, Finance, Sports & Videos](https://answers.yahoo.com/question/index?qid=20151111212739AAUBrzc) ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [November 12, 2015, 4:40pm UTC](https://boards.straightdope.com/t/math-help-please/737374/5 "2015-11-12T16:40:41Z")
> [@ElderSign](#): > > Same question asked last night: [https://answers.yahoo.com/question/index?qid=20151111212739AAUBrzc](https://answers.yahoo.com/question/index?qid=20151111212739AAUBrzc) LOLz at asking a limits proof question on Yahoo Answers. I’d be amazed if they could handle multiplying fractions. ---
**Author:** ![Drunky\_Smurf](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/drunky_smurf/32/449_2.png) [@Drunky\_Smurf](https://boards.straightdope.com/u/Drunky_Smurf)\ **Post date:** [November 12, 2015, 4:46pm UTC](https://boards.straightdope.com/t/math-help-please/737374/6 "2015-11-12T16:46:11Z")
> [@ElderSign](#): > > Same question asked last night: [https://answers.yahoo.com/question/index?qid=20151111212739AAUBrzc](https://answers.yahoo.com/question/index?qid=20151111212739AAUBrzc) Awesome internet stalking skills. Apparantly the answer is “v”. You’re welcome OP. ---
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [November 12, 2015, 5:12pm UTC](https://boards.straightdope.com/t/math-help-please/737374/7 "2015-11-12T17:12:07Z")
> [@ElderSign](#): > > Same question asked last night: [https://answers.yahoo.com/question/index?qid=20151111212739AAUBrzc](https://answers.yahoo.com/question/index?qid=20151111212739AAUBrzc) Identical, right down to the sign-off-“Thanks in advance!” ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [November 12, 2015, 5:22pm UTC](https://boards.straightdope.com/t/math-help-please/737374/8 "2015-11-12T17:22:03Z")
> [@brahmsacademic](#): > > How do you prove that the derivative of the sum as k goes from 0 to infinity of f(sub-k)(x) = the sum as k goes from 0 to infinity of the derivative of f(sub-k)(x). Thanks in advance! > [@friedo](#): > > Have you tried anything so far? This sounds like a homework question. > [@Chronos](#): > > Any proof is going to depend on your axioms. What axioms are you using about limits and sums? If I were you, I’d look for a good analysis textbook. If this _is_ a homework question, hopefully you already have one. Failing that, you might be able to google something up. I found PDFs [here](https://www.dpmms.cam.ac.uk/~agk22/uniform.pdf) and [here](http://www.math.ucla.edu/~tao/resource/general/131bh.1.03s/week45.pdf) that _may_ be of some help, but I didn’t have time to study them carefully. ---
**Author:** ![leahcim](https://avatars.discourse-cdn.com/v4/letter/l/b4bc9f/32.png) [@leahcim](https://boards.straightdope.com/u/leahcim)\ **Post date:** [November 12, 2015, 5:37pm UTC](https://boards.straightdope.com/t/math-help-please/737374/9 "2015-11-12T17:37:18Z")
The OP’s statement isn’t true in general, so there can be no proof. ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [November 12, 2015, 6:36pm UTC](https://boards.straightdope.com/t/math-help-please/737374/10 "2015-11-12T18:36:55Z")
> [@leahcim](#): > > The OP’s statement isn’t true in general, so there can be no proof. Yeah, that’s what I wanted to say. Here’s a trivial counterexample… Let f\_k(x) = 1. LHS is divergent while RHS is zero. ---
**Author:** ![Oukile](https://avatars.discourse-cdn.com/v4/letter/o/13edae/32.png) [@Oukile](https://boards.straightdope.com/u/Oukile)\ **Post date:** [November 12, 2015, 7:20pm UTC](https://boards.straightdope.com/t/math-help-please/737374/11 "2015-11-12T19:20:48Z")
> [@Lance\_Turbo](#): > > Let f\_k(x) = 1. LHS is divergent […] Is it? Sum over k of f\_k(x) is divergent doesn’t imply that d/dx(Sum over k of f\_k(x)) diverges. This is all about the proper formal way to define a limit. It looks a lot like the kind of exercises I had 20 years ago (and since my formal mathematics skills have taken some rust, I’ll leave it to other). ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [November 14, 2015, 1:53am UTC](https://boards.straightdope.com/t/math-help-please/737374/12 "2015-11-14T01:53:24Z")
This is obviously some exercise and some conditions are needed. Maybe boundedness; I don’t recall. I am an algebraist. ---
**Author:** ![leahcim](https://avatars.discourse-cdn.com/v4/letter/l/b4bc9f/32.png) [@leahcim](https://boards.straightdope.com/u/leahcim)\ **Post date:** [November 14, 2015, 2:51am UTC](https://boards.straightdope.com/t/math-help-please/737374/13 "2015-11-14T02:51:03Z")
> [@Hari\_Seldon](#): > > This is obviously some exercise and some conditions are needed. Maybe boundedness; I don’t recall. I am an algebraist. At the risk of doing someone’s math homework, the required condition is that the convergence of the series be [uniform](https://en.wikipedia.org/wiki/Uniform_convergence).