Is it useful to update the OS in my old MAcBook Pro? Knowing that I use the MacBook for programming, surf the web and write in latex do you think that the update to the new OS X version will provide me benefit in performance? 



Here the specifics of my MacBook Pro Mid 2010:
It is a tough question to estimate if you will get a performance boost from MacOS Sierra, as every system responds differently.

I have a mid 2011 iMac that I upgraded from El Capitan to Sierra, and I  found a noticeable decrease in performance. So much so that I rolled back and made a clean install of El Capitan.

There are however a number of good reasons to update. The first and most important being security. Apple will stop supporting and producing updates fro El Capitan soon. When this happens your system will become more vulnerable over time

I would recommend that if you do want to upgrade, back up your system to a Time Machine drive and disconnect it from the system before the update. If you decide that you want to roll back, you can follow a guide on making a clean El Capitan install here. Once you have done that, you can then restore from the Time Machine backup.