I don't really understand what you have written as an attempt? (x^2+1) in the beginning is to what power? Have in mind there are some cancellations in the end. You can really use the product rule, most of the times it makes things easier but I believe it is up to you. The other way is to use the...
I am new in the forum ( although I have read it for some time ) and I am not quite sure how much of a hint I am allowed to give you but:
You can prove that a set is closed using "balls". I would suggest you to work in this direction.