- I will try not to do that.
I won't try to do that.
I will try to not do that.
- 1. This is a positive sentence. The auxiliary verb is will and the main verb is try. Not does not qualify the main verb because it is not between the auxiliary and main verbs. Instead, it qualifies (or negates) the infinitive to do. So we have a positive idea that I will make a deliberate effort to avoid doing something - but there is the possibility that I will do it by accident.
2. This is a negative sentence because not is between the auxiliary and main verbs (I will not try). I will not make any effort to do it - and so it seems improbable that I will do it, even by accident.
3. The meaning of this sentence seems similar to 1, but the not is in the wrong position - in the middle of the infinitive to do. This is called "splitting the infinitive".