A sentence I found has the phrase "current trends in using business applications".
What does in using mean here?
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In using is not a constituent—a distinct part of the sentence.
A preposition phrase headed by in is the usual way of telling what kind of trend you are talking about. For instance, we speak of
trends in fashion
trends in music
trends in economics
trends in marketing
trends in programming
Note that last two trends have -ing words as the object of the preposition in. When an -ing form is used this way it is called a gerund—it acts as a verb and as a noun at the same time.
It can act like a noun in acting as the object of a preposition or a verb, or as the subject of a verb:
I live by writing. Writing is my profession. I enjoy writing.
It can act like a verb in taking its own subject (expressed usually as a possessive, but in some circumstances by an objective pronoun) and its own objects:
My writing answers gives me great pleasure.
In the sentence fragment you quote, using business applications is a gerund phrase—a gerund plus its object in this case—acting as the object of the preposition in. You might paraphrase the sense thus:
trends in how business applications are used