The answer is yes if you are using the truck for business purposes.
If you rent a truck to pick up day care equipment that is used 100% for your business, deduct 100% of the cost of the rental, including gas.
If you are transporting items used by your family and your business (patio furniture, appliances, hauling trash, etc.) deduct your time-space % of the cost.
Enter this expense on Schedule C, line 20a “Rent or lease.”