My great great grandfather naturalized in 1922, my great grandfather was granted a derivative citizenship through him in 1941. However,my great great grandfathers naturalization was cancelled in 1938... wouldnt that mean that my great grandfather could not have derived citizenship through him and would have had to apply on his own

What country are we talking about? It matters because they all have their own laws... and they can and do change over time.

He was italian I am american and I am looking into getting dual citizenship.

Going to have to wait for someone more familiar with the Italian Immigrations laws pertaining to that. THey have in recent years tightened up requirements significantly. I know that personally because I am elligible for citizenship there by virtue of marriage (met the residency requirements long ago), and am grandfathered into the old law.

Currently its never automatic or guaranteed anymore.

You could however contact the Italian Embasy and make inquireies into it.

If your father was born after 1948, the answer is "maybe"... depends on many factors. Need more info about your family tree and date they became naturalized, etc.