I was wondering what the differences are between these three: ～がたい、〜にくい、〜づらい

They all seem to be some sort of variant of "Hard to do ~". But it seems they
are used with different verbs and/or imply slightly different things. However,
I'm not sure on what these are.

Questions:

1) When should you use one of these over the others. For example, when should
you use ~がたい over ～にくい and ～づらい

2) What is the difference (and are all 3 acceptable?) between:

  1. わかりがたい 
  2. わかりにくい
  3. わかりづらい
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2011-09-25T06:14:20.413
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question
grammar word-choice nuances
The differences between ～がたい、〜にくい、〜づらい
Great question! Here's how I understand them:

### ～にくい 【～難い】

The most general of the three. Basic "hard/difficult to do ～" meaning.

### ～づらい 【～辛い】

You can see that it comes from `辛【つら】い` which can mean "difficult" or
"painful". So `～づらい` is usually a more subjective meaning, whereas `～にくい` is
usually more objective. Also, `～づらい` is limited to actions that are
intentional.

### ～がたい 【～難い】

Very difficult to do. "Virtually impossible". The most expressive of the
difficulty.

So I would say that `(～にくい <=> ～づらい) <<< ～がたい`. Also notice that `～にくい` and
`～がたい` have the same kanji. In practice, I don't think they're ever written in
kanji, but if you were to see it, I don't know if even the sentence context
would help you know which one it was.

>   2. What is the difference (and are all 3 acceptable?) between:
>

>   1. わかりがたい
>   2. わかりにくい
>   3. わかりづらい
>

Yes, they would all be acceptable, but would be used in different
scenarios/contexts according to the definitions (exercise left to the reader).

**UPDATE** ー According to the PDF posted by @Derek Schaab below, `分かりがたい` is
not acceptable because `分かる` is not an 意志動詞. However, `理解しがたい` is acceptable
in its place.

**NEXT UPDATE** ー I wanted to add this example that I've been thinking of for
a while. Hopefully it will be helpful to someone.

>   * [バンド名]の好きな曲は何？ → What is your favourite song by [band name]?
>   * 選びにくい………てか、選びづらいのだ。まー、やっぱりそれよりも選びがたい。 → (roughly) It's hard for me to
> choose....rather, it kind of hurts my brain to try to choose one. Actually,
> it's almost impossible for me to pick (which one).
>
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@istrasci's answer is very good but as an addendum, I would say that

づらい and にくい are not interchangeable because their nuance is very different.
にくい is more of a physical difficulty that everyone would experience where づらい
is more about an external social force or social norm that would prevent you
in particular to doing it. (Istrasci did slightly cover this point when
mentioning subjectivity)
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2011-09-26T04:32:51.110
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がたい is really formal and limited in usage compared to the others. For example:
信じがたい話 Someone's story that is hard to trust or believe.

づらい means that something is emotionally or mentally trying for the doer Thus
食べずらい would mean that is difficult to eat because it takes a lot of effort to
get through it.

にくい is the most general and often refers to physical limits or limits of one's
ability, be it situational or permanent. Thus 食べにくい can be used just as 食べづらい
with just a slightly different and more casual nuance as if just saying "it is
difficult to eat" in itself as opposed to it is difficult FOR ME to eat.

There's one more phrase that shares a common meaning and that is のは難しい which
is the polite non-slangy way to say something is difficult to do.
魚を食べることは難しいです。 It is difficult for me to eat fish.
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