She appears not to worry or she doesn't appear to worry Which one is correct??
They mean different things.
She doesn't appear to worry.
This means that there is no evidence of her being concerned. Perhaps she goes about her normal business, in her normal manner.
She appears not to worry.
This means that there is evidence that she is not concerned. Perhaps she participates in more upbeat activities than normal, or smiles more.
See also this question and its answers.