It depends on what you're looking for exactly. Derby.js is built on top of Express.js which has excellent support for creating a REST API. This also means that anything you can do in Express, you could also do in Derby. If you want real-time features, and the ability to build out a REST API, Derby.js is an excellent choice. It's also one of the reasons that people recommend Derby over something like Meteor (currently Meteor does not have support for REST endpoints, but it will hopefully in the future so also something you might want to keep your eye on, if you're in the market for real-time framework). However, if you're not looking for a node framework with an emphasis on real-time functionality, Derby is not the right choice. I would however recommend looking into Express.js to build a REST API. We use it currently for that purpose and it works really well. There are also a number of libraries and packages that play nicely with Express, so in the future if your needs change, it's easy to find something that works well with Express.
Anyway, I would recommend checking out some basic tutorials for how to create a REST API in Express because once you're able to successfully do that, adding some of the real-time features of Derby.js is fairly straightforward.
Basic tutorial on creating a REST API in Express.
http://coenraets.org/blog/2012/10/creating-a-rest-api-using-node-js-express-and-mongodb/