I am a data science freelancer and I mostly do projects for IT-dominated companies. First, I was surprised that such companies need some external help with relatively simple tasks; only later I discovered that top-notch performance in webdev (or even: algorithms) does not mean that someone is able to do simplest data analysis.
For data science / ML - I know a lot of openings in which they are looking for "data scientists", but what they mean is software engineers with at least a slight idea what is data analysis.
When it comes to deep learning in particular - I don't know.
I've been wanting to get into this field recently. Do you have more info about these openings, perhaps?
When 3 years ago I was looking for data science internships, most of interview were strictly in software engineering. (I got into a more data-analysis oriented.) Even when I applied to Google a year ago (and failed), all non-trivial questions where in software engineering (some with data-oriented paradigms, tough).
Look at https://medium.com/@rchang/my-two-year-journey-as-a-data-sci... - the taxonomy of "Type A Data Scientist" vs "Type B Data Scientist" is useful. You want to apply for the "B" or even - software engineer in a company which deals with data and is open to shifting roles.
Going back to the interviews: I see that the set of questions is entirely different. E.g. if the first question is "how to invert a binary table" or "how to test if a black-box number generator is fair". But sometimes it is not clear from the job opening.
EDIT:
If you are interested in my background: http://p.migdal.pl/2015/12/14/sci-to-data-sci.html
I personally took several ML courses from coursera/udacity/edX, and they helped me when I decided to move to another group that works on the ML-related projects.
Most other programmers wouldn't be able to contribute much value in a world that worked like this.
This perhaps mirrors how the chip market works, which similarly involves a limited number of researchers involved in advanced manufacturing techniques that are highly specialized and mostly a mystery to other people in the technology field.
I'm not sure that a deep learning course would be a good first course. But an intro course on linear regression and basic probability/statistics would be worth looking into.