Determine compatibility between CUDA driver version and CUDA Toolkit version

Is there an easy way to determine whether a new version of the CUDA toolkit will be compatible with an installed CUDA driver?

Specifically, the driver is v10.1.x, but I’ve had problems with the corresponding version of the toolkit.
If I install the current v10.2.x toolkit, will there be conflicts with the 10.1.x driver?

Make that driver version: 418.87.00

Perhaps there is an easy way to update the driver so I don’t have to worry about compatibility? I’ve heard that driver updates are simpler as of CUDA version 10.

A newer driver is compatible with an older toolkit.

refer to table 1 in the release notes:

In this case, it’s the reverse: newer toolkit, older driver.
So it looks like I’d need to update the driver (currently
418.87.00) in order to load the newer toolkit (10.2.x).

Given the problems I had with the initial driver installation,
I was hoping to avoid that.