What to use in the following sentence?
You need to believe in yourself and not to/not/don't give up after the
first failure.
It seems to me that the correct option is the first one, but I can't explain why and am not even sure if it really should be not to.
Best Answer
The preferred formulation is: "You need to believe in yourself and not give up after the first failure." The formulation with "not to" is also accepted.
Here are a few examples found "in the wild" (emphasis added); the last example uses "not to":