Windows comes with commands to do that (command prompt = dism /online /export-driver /destination:"path of folder" : powershell = Export-WindowsDriver -online -destination "path of folder")
Having said that I'd question the need to backup drivers rather than simply saving a copy of the drivers you've downloaded due to a lot of Windows drivers coming with their own applications for changing settings, something a simple backup of drivers will miss as it does what's on the tin. It would backup the drivers and drivers only, it would not include any of the software that gets installed along with those drivers.
I use the PowerShell command to backup drivers before a reinstall.
Windows update will install driver updates for motherboard components, which sometimes the motherboard manufacturer doesn't make available on their website, meaning you have to go searching for them elsewhere, e.g. Realtek NICs
It's also quicker to install the drivers, using the "Add drivers" option at the top level of Device Manager and pointed to the exported drivers folder.
Or as I do, after a tip on these forums, add the drivers to the install.wim file.
Find the index for the edition, e.g. Home, Pro
Code:
dism /Get-ImageInfo /Imagefile:T:\WIM_Source\install.wim
Mount the WIM with the index number of the edition you want to add the drivers
Code:
dism /Mount-Image /Imagefile:T:\WIM_Source\install.wim /index:6 /Mountdir:T:\WIM_mount
Add drivers from the exported folder
Code:
dism /add-driver /Image:T:\WIM_mount /driver:T:\WIM_Drivers /recurse
Optional: Add security updates downloaded from the updates catalog
Code:
Dism /Image:T:\WIM_mount /Add-Package /PackagePath=T:\WIM_Updates
Unmount
Code:
dism /Unmount-Image /MountDir:T:\WIM_mount /commit
Optional: You can use the original install.wim, but I like to export just the edition I need.
Code:
dism /export-image /sourceimagefile:T:\WIM_Source\install.wim /sourceindex:6 /destinationimagefile:T:\WIM_Export\install.wim