Do real life economists and financial analysts actually use calculus in their jobs? From what I understand a lot of calculus is used at university level when studying economics and some finance courses (correct me if I'm wrong) but I was just wondering if economists and financial analysts actually use calculus in their actual jobs on a day to day basis.
Yes, whether you do research and you need to study a new model and characterize optimal behavior, or if you are studying data and you are estimating any model that is not linear you use calculus on a regular basis. 

Even though computers are very powerful and can save the time and energy of doing calculations (including finding derivatives), often times having a firm knowledge of the maths behind what the computer is doing can save tons of time and improve the performance of algorithms.

That being said, it is also true that many economists can get by only knowing the minimum of calculus, since a lot of the tools that the market values the most from economists require, instead,  a firm grasp of probability, statistics and good economic intuition.