Technically, any income you earned making deliveries in Detroit is subject to Detroit City Income Tax.
Based on the information you provided, the amount you earned "in Detroit" would be very difficult to calculate. You would need a detailed log showing which deliveries were to Detroit and and what the mileage & other costs for those deliveries were. The net income from those "few" jobs would probably be immaterial (too small to be concerned with).
From Detroit City Individual Taxes:
City income tax rate for Non-Resident Individuals - 1.20% on all income earned in the City
What income is taxable: For Non-residents - Salaries, wages, bonuses, commissions, or other compensation for services rendered for work done or services performed in Detroit; net rental income from real and tangible personal property located in Detroit; net profit from a business, profession or other activity as a result of work done, services rendered or activity conducted in Detroit; capital gains less capital losses from the sale of real or tangible personal property located in Detroit.
