I wanted to say that someone's project has some dependencies on my previous work and that project reuses some part of my work. Which word or phrase should I use?
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Most open source licenses (and copyright law) would refer to a project that reuses and depends upon your previous work as a derivative work.
So [as FF mentioned] the newer project is derivative of your previous project; it derives from yours.
I would say that "builds upon" would be the most natural construction here, assuming you were trying to convey the meaning that it wouldn't have been possible without the earlier work without trying to implicitly convey that it is derivative in nature.