A B737 CREW DEPARTING DFW MISSED A PDC CLRNC CHANGE ASSIGNING A SID. BOTH PILOTS HAD EXAMINED THE PDC CAREFULLY. FATIGUE MAY HAVE BEEN A FACTOR.

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WE RECEIVED PDC VIA ACARS AND NOTICED A REVISED SEGMENT. REVISED SEGMENTS ON CLRNCS ARE RECEIVED OFTEN AND ARE USUALLY DIFFERENT VERBIAGE TO MEAN THE SAME THING -- USUALLY ADDING A VOR ON THE AIRWAY THAT WAS NOT LISTED ON THE CLRNC; BUT WOULD HAVE BEEN PASSED OVER ANYWAY. WE LOOKED AT THAT PART OF THE CLRNC AND AGREED THAT THERE WAS NO CHANGE. BUT REALLY THERE WAS. WE HAD BEEN FILED ON THE DALLAS 8 DEP; BUT ON THE REVISED SEGMENT; THE DEP WAS CHANGED TO THE CLARE 2; WHICH WE DID NOT NOTICE. CLBING THROUGH ABOUT 6000 FT; THE CTLR GAVE US A LEFT TURN TO JOIN THE DEP AND SAID; 'IT LOOKS LIKE YOU MISSED YOUR TURN.' WE THOUGHT WE WERE ON VECTORS AND WERE WAITING FOR DEP TO TURN US; BUT WE SHOULD HAVE BEEN ON THE RNAV DEP AND ALREADY TURNED TOWARD THE EAST. I BELIEVE A FEW FACTORS CONTRIBUTED TO OUR OVERSIGHT. FIRST; THE REVISED SEGMENT CLRNC HAPPENS ALL THE TIME; BUT NOTHING HAS REALLY CHANGED; SO OUR GUARD WAS DOWN. SECOND; WE HAD A XB30 SIGN IN AND I GOT UP AT XA00. ALTHOUGH I WENT TO BED EARLY WITH ENOUGH TIME TO GET A GOOD NIGHT'S SLEEP AND SET TWO BATTERY POWERED ALARMS; I DID NOT SLEEP WELL; SO I WAS TIRED EVEN THOUGH WE WERE JUST STARTING OUT. NEITHER OF THESE REASONS ARE AN EXCUSE FOR MISSING AN IMPORTANT DETAIL; AND IN THE FUTURE; I WILL BE MORE DILIGENT IN CHECKING REVISED CLRNCS.SUPPLEMENTAL INFO FROM ACN 792576: POSSIBLE CONTRIBUTING FACTOR WAS VERY EARLY SIGN-IN WITH SIX HOURS OF DISRUPTIVE SLEEP.