MLG ACFT DEPARTING; RWY CHANGED AS ACFT WAS BEING DEICED; CLRNC DELIVERY ISSUED REVISED DEP INSTRUCTIONS. RPTR CAPT MISUNDERSTOOD THE CLRNC AND SET AN INTERCEPT HDG IN THE FMS AND BRIEFED FO AT 400 FT THEY WOULD USE LNAV. NEITHER PLT READ THE NEW SID CAREFULLY AND DURING CLB WERE QUESTIONED ABOUT HDG. RPTR CAPT ATTRIBUTES LONG HRS OF FLYING IN THE PRECEDING WK PLUS ILLNESS RESULTING IN FATIGUE.

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FLT ORIGINALLY CLRED IFR SALT LAKE 5 SID DEPARTING S OVER FFU. WHILE DEICING AT REMOTE PAD; DEPS CHANGED TO THE N. AFTER DEICE AND ENG START AND PRIOR TO TAXI; WE GOT VERBAL CLRNC FROM CLRNC DELIVERY (TO THE AFFECT -- I DO NOT KNOW EXACT WORDING) '...SALT LAKE 5 TO THE SLC 094 DEG RADIAL TO THE MTU 300 DEG RADIAL AS FILED; MAINTAIN 11000 FT.' I MISUNDERSTOOD CLRNC TO MEAN '340 DEG HDG TO INTERCEPT SLC 094 DEG RADIAL.' ON TAXI OUT; I BRIEFED THE FO THAT THE SLC 5/SLC 094 X MTU 303 WAS IN THE FMS AND THAT I WOULD BE CALLING FOR LNAV AT 400 FT AGL AFTER TKOF TO FOLLOW FLT DIRECTOR COMMANDS FROM LNAV. AFTER TKOF LNAV FLEW THE 340 DEG SID HDG TO THE SLC 094 DEG AND SO ON. DEP CTL ASKED WHERE WE WERE GOING AND IF WE HAD TERRAIN IN SIGHT (MOUNTAINS TO E). IF CLRNC DELIVERY HAD SAID SLC 5 'RADAR VECTORS TO THE SLC 094 DEG' OR TWR HAD SAID 'RWY HDG' WE WOULD NOT HAVE TURNED. HOWEVER; THE MANNER IN WHICH THE CLRNC WAS DELIVERED MADE US THINK 340 DEG HDG TO INTERCEPT THE 094 DEG OUTBOUND. OUR RTE WAS NOT DEPICTED ON THE SID. HAD I READ THE SID MORE CAREFULLY PRIOR TO MOVING THE ACFT OR THE FO READ THE SID MORE CAREFULLY WHILE I TAXIED/BRIEFED THE DEP WE MAY HAVE BECOME CURIOUS ENOUGH TO QUESTION THE PROC. PERHAPS IF CLRNC DELIVERY/TWR HAD NOT OMITTED CERTAIN KEY WORDS WE WOULD NOT HAVE MENTALLY MISPLACED THOSE OMISSIONS WITH OUR OWN BELIEFS/EXPECTATIONS (CRM). ALSO CONTRIBUTING: 39+9 HARD TIME AND 6 MONTHS CHK IN PREVIOUS 9 DAYS (2 DAYS OFF). SHORT NIGHT REST (9+45 BLOCK-TO-BLOCK) AND FIGHTING CHEST INFECTION FOR LAST MONTH (FATIGUE?).