You are licensed by Apple to use the music, jingles, and sound effects included with Final Cut Pro X in your videos on a royalty free basis.
You can use the audio content for personal or commercial use. (For details, see the license. I am not a lawyer)
For your license, see this document, http://images.apple.com/legal/sla/docs/FinalCutPro.pdf
However, an annoying part of using YouTube is that sometimes others will claim that you are infringing their copyrights if you use Apple's licensed music. You can dispute this with YouTube by providing the Apple license information, and they will usually back down. Instructions for disputing the claim are below.
It is also a good practice to proactively put a "credits" title at the end of your video, stating music you have used and the source. You can also reference this in the description of your video, and perhaps in your Adsense settings for the video. The copyright violation algorithm is automated, so none of this will stop your video from getting flagged, but it will help you remember where you got the music and how you are licensed.
For more on this irritating problem and why it is so hard to solve, see this article by Larry Jordan.
Here is a good article in ArsTechnica. http://arstechnica.com/tech-policy/2012/10/youtube-finally-offers-a-meaningful-c ontentid-appeal-process/
Also see YouTube Blog Post here. http://youtube-global.blogspot.com/2012/10/improving-content-id.html
To dispute the claim with YouTube, sign into YouTube.
Click on Video Manager (to see my videos that I have uploaded.)
Click on the Copyright notices link.
I see a link under the thumbnails which says "matched third party content". Click on this link.
Click on the link that says"I believe that this copyright claim is not valid."
Check the box that says I have a license or written permission from the proper rights holder.
You may get a box that enables you to explain. State that "I am licensed by Apple, Inc. to use "track name here" which is provided in the Final Cut Pro X App from Apple, Inc." Put a link to the Apple license.