Relax
no stress and no need to plan in advance
Gates are allocated during the descent, so no way to know this in advance. Your 2 flights arrive/depart from 2E at one of the 3 concourses (K, L or M). When you will disembark from DEL, just check your gate for DTW on the monitors or on a kiosk and follow the signs for your new concourse. Very easy to navigate between those 3 concourses. You won't have to go through passport control but you'll have to pass security.