How Smooth is Upgrading Linux kernel in Debian 8.5?

I would like to upgrade my Linux kernel to 4.7 in Debian 8.5, since it has significant better Skylake 6th generation support than the current linux kernel. In Ubuntu 16.04, the upgrade is easy. However, I now need Debian 8.5 because of stability, and I would like to do the same upgrade for it. Testing StephenKitt's answer --- I upgrade the kernel and reboot, but I get unsuccessfully when loading the OS. Fig. 1 Failure messages in startup 2nd iteration - Solving the Bug in startup [GAD3R] --- 1. Boot in Linux kernel 3.16.x 2. Run as su, apt-get remove xserver-xorg-video-intel 3. Reboot Output: works! Resolution is now the 1920x1080. Since there is no complete support of Skylake in Linux kernel 4.6 etc this artifact here in Matlab 2016a without a firmware, you need some non-free adjustments as firmware; which you maybe already free firmware in Linux kernel 4.7 # https://unix.stackexchange.com/a/307435/16920 apt-get -t jessie-backports install firmware-misc-nonfree xserver-xorg-video-intel abnormal installation and its action's prevention --- I find out that the package xserver-xorg-video-intel may get installed as a dependency (and all its dependencies) in other conditions, as described a case in the thread How to Recover Debian of LK backports where runlevel conflict? The idea is to prevent the action of the package although it get installed by creating the file /etc/X11/xorg.conf # https://unix.stackexchange.com/a/308709/16920 Section "Device" Identifier "Intel" Driver "modesetting" EndSection ## Bugs # 1. LK 3.16 will fail now but LK 4.6 will work. TODO in the thread https://unix.stackexchange.com/a/308709/16920 Hardware: Asus Zenbook UX303UA OS: Debian 8.5 Related: Asus Zenbook UX303UA Linux compatibility , Linux Kernel - Mobile Skylake 6th Generation - Power Management