I have an 11 speed cassette 11-32 teeth. I am running a 52 teeth chainring on the front. What would be a good recommended smaller chainring for the front? It needs to be big enough to take up the slack of the chain when i am on the smallest cog at the back.
As was mentioned in the comments, this question will depend on what derailleur you are using both front and rear (since they have a rated capacity). Too large a difference and the front derailleur will not shift well, but you also have to make sure the the total difference between large-large and small-small is within the range of the rear derailleur so that it takes up the slack and does not overextend. The specifications for your derailleur should have these numbers listed and then you can pick an appropriate sized ring to fit your crank from there.
You'll generally want to get the smallest inner chainring possible, in order to maximize the spread of gears. The actual size of that chainring will be determined by your crank's BCD (bolt-circle diameter). It's impossible to say what size your BCD is, although with a stock 52t big ring I would guess that it's a road standard size, 130mm. This means your smallest available inner ring is 39-tooth. 52/39 is a modern standard combination, and 52/42 is an older standard; either will work.
I wouldn't worry too much about your derailer capacity and chain slack. If your rear derailer can accommodate a 32 tooth cog, it must have a medium or long cage, both of which are capable of "wrapping" plenty of chain. The only instance in which chain slack becomes an issue is when combining the inner small chainring with a small cog on the cassette. This combination is horrid for your drivetrain, and ought to be avoided at all times.
If you are worried about chain slack because of dropping a chain, that is a separate issue, largely unrelated to derailer/chainring compatability. 1) dropped chains are a fact of life. get used to "picking up" a chain using the front shifter to avoid having to get off the bike. 2) if it's a mechanical problem, your limit screws may be improperly set. 3) don't shift under heavy load. if you shift into a low gear while you're already climbing the hill, you're doing it wrong and you're breaking your parts. shift BEFORE you need the gear you want to be in.
sorry for the pithy attitude, i've had a few beers and am striving for clarity.
edit: if your cranks end up being 110bcd (compact BCD), you can go pretty low on your inner ring. You could even do a 52/34 (I do!), but you must accept tricky front shifting.