The IRS can deny your deduction if you don't have written evidence supporting the deduction.   Keep mileage logs.  You don't have to submit the logs with your return, but if your return is selected for a review or audit, they will want to see the logs.   And if you don't have them or can't reproduce them, they will deny the deduction.  

It is important to keep all documents used to complete your tax return. The documents kept should include records supporting the income, expenses, deductions or credits you claimed, such as invoices, receipts, mileage logs, and checking account statements showing amounts paid, and any other proofs of payment. The records should be well-organized to answer any questions when your tax return is selected for audit. The records supporting items on your tax returns should be kept for at least three years after filing your tax return.