All three are acceptable.
The thing to watch out for is whether or not the different parts are parallel.
This my be easier to demonstrate with an incorrect case, than a correct one:
?His results, derived both from researching and observation, are critical for the project.
Because the gerund form researching doesn't match the noun form observation, this is less eloquent than the examples you have, where you use the noun form research.
This wouldn't be incorrect as such (just how far out a break in parallelism has to go to be incorrect, if it can at all, is debatable), but it can be jarring.
Your cases are okay in this regard.
Some other problems with parallelism can only happen with three or more parts:
?His results, derived both from research, from consultation with colleagues and observation, are critical for the project. [Please forgive this not really being a sensible thing to say here, I'm looking at the grammar only].
This comes close to your concern, as some of your examples repeat the from and some do not. In the above less graceful example (and this bad enough that some might consider it actually incorrect rather than merely clumsy), I repeat the from in one case and not another. Of course, that can't happen when you've only two items; either you'll repeat it or you won't.
In all, it's purely a matter of style. Repeating from emphasises the relationship between the results and the source, and might be worth using for that reason. The other two have an advantage of being slightly more concise, without being so at the expense of causing confusion.
…both from… would be slightly less usual than "…from both…", but this emphasises the both and as such the fact that there are two sources, precisely in being slightly unusual (it leads the reader to pause and focus slightly). As such you might want to avoid it as unusual, or just as reasonably favour it for that emphasis.
These though are rhetorical decisions; grammatically all three are fine.