You can update Ubuntu to the latest kernel very easily using apt-get.
To generate a list of available kernels run…

# apt-cache search linux-image 

This will create an extensive list on Ubuntu 14.04 LTS, so I have picked out the latest to give three examples…

linux-image-3.19.0-58-generic - Linux kernel image for version 3.19.0 on 64 bit x86 SMP
linux-image-extra-3.19.0-58-generic - Linux kernel extra modules for version 3.19.0 on 64 bit x86 SMP
linux-image-4.2.0-35-generic - Linux kernel image for version 4.2.0 on 64 bit x86 SMP
linux-image-extra-4.2.0-35-generic - Linux kernel extra modules for version 4.2.0 on 64 bit x86 SMP
linux-image-4.4.0-21-generic - Linux kernel image for version 4.4.0 on 64 bit x86 SMP
linux-image-extra-4.4.0-21-generic - Linux kernel extra modules for version 4.4.0 on 64 bit x86 SMP

Depending on which version you would like to install, run one of these commands…

linux-image-3.19.0-58-generic…

# apt-get install linux-image-3.19.0-58-generic linux-image-extra-3.19.0-58-generic

linux-image-4.2.0-35-generic…

# apt-get install linux-image-4.2.0-35-generic linux-image-extra-4.2.0-35-generic

linux-image-4.4.0-21-generic…

# apt-get install linux-image-4.4.0-21-generic linux-image-extra-4.4.0-21-generic

And reboot your server.

You can then run…

# apt-get autoremove

To clean up any old images, it may not find any right away, but you will be reminded at a later date.