"try not to make a sound" or "try to not make a sound"

[lagoo]

I came across these two sentences as follows:

1. We are doing the right thing to not give up on him.
2. Try not to make a sound.

Are these correct?
If so, why do the negations of the infinitives locate differently?
In sentence (1), is it acceptable to move “not” before “to”?

 

[Rover_KE]

In #1, 'not' would sound better before 'to'.

 

[emsr2d2]

I would find #1 more natural as "We are doing the right thing by not giving up on him".