B737-300 CAPT TURNED INTO THE WRONG GATE. THE CAPT WAS SUFFERING FROM CUMULATIVE FATIGUE.

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THIRD LEG OF THE DAY; LAST LEG OF 2-DAY TRIP. LANDED RWY 35R; TAXIED TXWY P7; TXWY ED; GIVEN CLRNC TO ENTER AMP. ATTEMPTED TO TURN INTO ALLEY WAY FIXATED ON ARRIVING AT GATE (EARLIER GATE SMF-DEN FLT THAT MORNING). ON SOME LEVEL; I KNEW THAT WE WERE ASSIGNED XXX (SET 000 IN COURSE SELECT WINDOW FOR VOT CHK). NONETHELESS I ATTEMPTED TO TURN INTO WRONG SIDE OF RAMP. MY FO HAD TO VERBALLY REMIND ME OF THE GATE; AND PHYSICALLY HAD TO TOUCH MY L ARM TO GET ME TO RESPOND TO HIS INSTRUCTIONS. I BELIEVE THE ROOT CAUSE OF THIS ERROR HAS BEEN MY INCREASING LEVEL OF FATIGUE; COMBINED WITH THAT DAY'S 2.5 HR SIT IN DEN AFTER ARRIVING FROM SMF. I'M AN LCA; AND EXTREMELY TASK DRIVEN TO GET THE PEOPLE TO DEST EFFICIENTLY AND SAFELY; BUT I BELIEVE MY PWRS OF CONCENTRATION HAVE BEEN DIMINISHING. AT THE COMPLETION OF THIS TRIP; I BELIEVE I WAS TOO FATIGUED TO FLY MY NEXT ASSIGNMENT WITH 13 HRS OFF DUTY; AND CALLED IN SICK. I AM DILIGENT IN MY WORKOUT AND NUTRITION REGIMES; BUT BELIEVE THE CUMULATIVE EFFECT OF THE FLYING I'VE BEEN DOING; COMBINED WITH THE BAD WX IN DEN THAT MORNING AND THE DAY BEFORE LEFT ME BARELY ABLE TO FUNCTION ON THE FLT DECK.