There are quiet a few things to try in the following order.
1) if it was an official update, and your device is under warranty, then get it repaired.
2) try a factory reset via recovery. Search to find the key combination to get into the recovery and Perform a factory Reset.
3) Android Marshmallow has the ability to grant/restrict specific permissions to apps. Make sure that all system apps and Google apps have all the permissions granted.
4) this step is recommended only if you have some knowledge about the working of an Android device. Connect device to a computer and check the logcat to find what went wrong. try to fix the error that caused the issue.