If the partnership does not own the car, then the partnership cannot take a deduction for depreciation on the car.
if you want the vehicle expenses to be deductible on the partnership return, then the partnership must reimburse you for those expenses either using the standard mileage rate or actual expenses based on the business mileage. commuting is considered personal mileage. you need to submit a report to the partnership for reimbursement. failure would likely result in disallowance if audited.
or you want to take the business use on your personal return there is a section/question about unreimbursed partnership expenses which are really for the partner. having documentation in case you're audited is important, especially mileage.
if the partnership agreement specifies how these expenses are to be handled you must conform to the agreement