There are multiple ways to disable this "feature". Here in EU it isn't allowed to have cameras that don't make sounds when taking a picture because you could sneak pictures from people and so. Basically, the option to turn off sound is implemented in the camera software. But the files initiallizing the app on start up tell the software to show or hide this option. That said, you can try to use an app to disable the stock app sound, you can manually change settings in the files that tell the camera what to do (as easy as adding a line of text or even just changing one bit from 0 to 1 or vice versa) or you can use an Xposed module like wanam where there's an option for this that can easily be toggled.
So far I haven't heard of a method that works if you're not rooted, so root seems to be mandatory if you want to do this.
If root isn't your thing, check out other picture taking apps in google play. There are certainly apps that allow to disable shutter sound, and some of those apps provide more/better camera functionality than the stock app. Dpreview.com is a great photography site which also has a mobile phone section called connect. There you get in depth reviews on phone's cameras and apps from a photographers point of view.