If you do not own or lease the vehicle you can't use the standard mileage rate.  That's because the standard mileage rate includes an allowance for depreciation (wear and tear) and only the owner or lessor is allowed to claim that.

You have to use the actual expense method for this vehicle.  You need to add up the total expenses for the year -- gas, oil changes, tires, insurance, other maintenance (but not depreciation).  And you also need to track the miles used for work purposes and the total vehicle miles for the year (beginning and ending odometer).  You deduct the percent of actual expenses based on percent of work miles driven.  

TurboTax will do all these calculations for you.  You need to know the number of work miles driven, the number of total miles driven or the start and end odometer, and the total of all actual costs for fuel, etc.

If you are an employee and you are asking about the tax year 2018  you are no longer able to deduct unreimbursed business expenses. Only independent contractors are able to deduct expenses  under the new tax laws.  Even in the past years you would have not been able to deduct commuting costs-just the miles driven while at work. In the past you could deduct miles driven between two jobs-now with one a W2 jog and one a 1099 job  I am not certain. 

 If your second job is as an independent contractor then you would be able to deduct the use of your vehicle for that job. https://turbotax.intuit.com/tax-tips/self-employment-taxes/standard-mileage-vs-actual-expenses-getti...

You can BUT ... read the rules...

https://www.irs.gov/faqs/small-business-self-employed-other-business/income-expenses/income-expenses...