Independent/independently of/from

Independently of is correct here. To be independent of something means to not depend on it for anything essential. Hence, the following is the best choice:

[Noun] was developed independently of [noun].

Independently from is not correct usage, as well as being very uncommon. From X would indicate either coming from X or going away from X, neither of which applies here, since independence does not come or go from something.

The third option, though decipherable, does not mean exactly the same thing since independent could just as easily be referring to the [noun] as to the development, creating an ambiguity, as well as an unnecessary comma. Both of these should be avoided whenever possible.