You can either claim the simple mileage rate or actual vehicle costs, not both. Actual vehicle costs include gas, repairs, maintenance, necessary modifications, and the purchase or lease of the vehicle itself.
Track both your vehicle expenses and your daily mileage to determine whether one or the other would result in a larger deduction. Given the high volume of miles driven for deliveries, the mileage deduction is likely to be favorable to most drivers. But if you incurred large repair bills or you purchased or lease a car specifically for delivery purchases, then the deduction of the actual cost may be larger.
Note that you can only deduct the percentage for which the vehicle is used for delivery/business purposes, so when calculating the actual costs of something like repairs for a vehicle you use 50% for personal use, then you will divide the cost of repairs in half.