The iPhone automatically backs up some data to iCloud or your computer, but this data does not include playlists you've created on your phone. As long as you enable syncing music between your phone and computer, iTunes imports your iPhone playlists, but it does not store multiple backup copies as it does with data backups. For additional security, you can manually export your playlists through iTunes.
Every time you sync your iPhone with iTunes when "Sync Music" is checked, it copies copy playlists you've created on the phone into iTunes. This can serve as a backup if you have to restore your phone, but if you delete or modify the playlist on your phone, that change will also sync to iTunes.
To create a true backup that iTunes won't automatically overwrite, you can export a playlist directly from your iPhone to a file. Connect the phone to your computer, open iTunes and click the phone's name. Press "On This iPhone" to see your playlists. If you have the iTunes sidebar enabled or use a version of iTunes prior to 11, open the drop-down menu by your phone's name to see the same list. Right-click a playlist and pick "Export." You can choose either a TXT, XML or M3U file. ITunes can import any of these files, but if you want to restore to another program, check its compatibility.
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