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The Yamaha P515 has s USB audio interface which means that if you have an iPhone and the USB to lightning adapter (AKA Apple Camera Connection Kit), you can connect the piano through only a simple (printer) USB cable to the adapter and the iPhone and when shooting videos the digital piano sound will automatically be used instead of the microphone.
For my better videos I usually record the audio on a USB thumb drive inserted in the piano, while shooting the video with my Fuji X-E3 camera and then I combine the video and the audio in iMovie on my Mac. If you go that way, let me know and I can help.
For some even better audio/video I usually use my N1X as a MIDI controller to Garritan CFX. If you go that way, there are many options, for instance you can set Garritan CFX to record a WAV file on the computer disk. Then I combine the audio with the video.
I've recently discovered a very elaborate but elegant way to directly record the video from my Fuji X-E3 combined with the audio from Garritan CFX on my Mac, however it requires additional adapters, such as a HDMI to USB adapter and the actual recording is with the QuickTime Player on my Mac which can be configured to record video from a selected video source and audio from a selected video source, this way all is properly combined. You can use that method also for recording from your P515.