Date: 201808
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Light: Daylight
Aircraft: Medium Transport; Low Wing; 2 Turbojet Eng
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Taxi
ATC / advisory: Tower ZZZ
Reporter organization: Air Carrier
Reporter function: Captain
Reporter qualification: Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Human factors: Situational Awareness; Communication Breakdown; Fatigue
Anomaly: Deviation / Discrepancy - Procedural Clearance; Ground Incursion Taxiway
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Became Reoriented
Contributing factors: Airport; Chart Or Publication; Human Factors
Primary problem: Human Factors

Narrative: In ZZZ we were given the instructions to taxi XX to the intersection of XXR and XX1 for takeoff. While on XX1 at the hold short line for XXR the FO (First Officer) said; 'You are on XX2 not XX1;' I looked up and did see an XX2 location sign out to my left; at this time we were cleared to line up and wait from XX1; which added a bit of urgency; I immediately repositioned on the next taxi way over where the FO had pointed to; and entered the runway from there. We lined up and took off without incident; ATC didn't say anything about it; but the whole thing didn't seem right and once we got to altitude I reviewed the taxi diagram again; and recalled a couple of other things. We had absolutely been on the correct taxi way; XX1; the first time; I had even remembered saying while on XX; 'Here is X20; XX1 is next;' and then being at that taxiway behind another aircraft which was cleared to takeoff from XX1. So the FO was incorrect and we actually moved from XX1 (the correct taxiway) to XX2 (the incorrect taxiway) when we did what he said. The reason we saw the XX2 location sign was because it was between XX1 and XX2; so we were not actually on XX2. I absolutely believe my incorrect response to the FO's allegation was 99% fatigue related.I had a day trip; a four day; and another day trip lined up for a total of six days on and this happened on the last leg of day six. The four day in the middle was mentally and physically exhausting; and after two close to minimum rest overnights; I started my day-trip on day six with an early morning turn; then a two and a half hour sit with an ZZZ turn left to go. I considered calling in fatigued on the sit due to how out-of-it and exhausted I was feeling; but after grabbing a cup of coffee I felt decent and decided to press on; only to find out when I got to the plane that the FO I would be doing the last two legs with was on his first leg off of IOE (Initial Operational Experience). I'd been expecting a senior FO; so at this revelation I immediately regretted not calling in fatigued; which in hind sight; is the wrong approach to take to fatigue. Whether or not I call in fatigued should not be based on who I am flying with; I should not expect a senior FO to carry part of my weight or 'keep an eye on me;' I'm either fit to fly or I am not; and if I'm not alert enough to fly with a brand new FO then I'm not alert enough to be flying. At this point calling in fatigued would have no doubt meant delaying passengers and the crew; which I try to be considerate of and avoid; but in the interest of safety I should not have let it stop me from calling in fatigued either.Had I not been exhausted and already a little on edge from a couple of stupid little things I did from being so worn out (like trying to taxi with the parking brake on); then immediately swooping over to the next taxiway; just because someone who has been on the line for two weeks told me it was the right one with confidence; would not EVER have been my response. I know much better than this and I feel my normal response to this situation would have been to tell tower we needed a minute; and for the FO and I to review the taxi diagram and our location together. The intersection we did takeoff from gave us more runway; so it was not a performance hazard in this instance; but it was still a deviation from an ATC clearance and could have been worse.Fatigue was the main factor for this incident. Some other minor factors were that I am a newer captain; in my three months as captain it has just worked out that I have worked with mainly senior FOs and other reserve captains (which isn't to say that a senior person couldn't have made the new FOs mistake; just that I need to make sure I don't let working with experienced/knowledgeable pilots allow me to develop complacency when it comes to listening to the person I'm working with; we BOTH need to stop and see regardless of their experience level).I've flown while tired; but this is thefirst time I've ever flown fatigued; I learned a lot from it and absolutely won't hesitate to call off fatigued in the future if I think I'm nearing this point.




Synopsis: Captain reported fatigue led him to depart from an incorrect intersection from which he was cleared for takeoff.