Something like - your car cost $30,000 and depreciates over 10 years, so $3,000 per year (just making up numbers, no idea if/how the IRS depreciates a car). So you'd have a $3,000 loss in the value of the car per year until it drops to 0. If the car was used 40% of the time for business (driving for Uber) you could claim 40% of the depreciation - $1200. I guess then you'd have to separately itemize all the gas, maintenance, etc.
But if you're actually losing money on the Uber-driving endeavor when that is factored in, whatever revenue you get should be tax-free. Of course, I suppose that only works if you're an independent contractor / business, and Uber drivers fought so hard to get treated as employees instead. Oh well. Employees get screwed when it comes to taxes.
Example 10-mile trip: 1.25 base fare + (10 miles * 1.15 per mile) = 12.75 * 80% (driver's share) = $10.20 revenue - 5.40 deduction for mileage = $4.80 revenue reported. For somebody in 20% tax bracket, this could yield $1.08 in savings.
Although using the per-mile deduction negates the ability to deduct line item expenses, such as gas, car washes, etc.