CTRL + W usually deletes everything until the previous whitespace, so it would delete the whole '/var/log/nginx/' string in OP's example. Alt + backspace usually deletes until it encounters a non-alphanumeric character.
Be careful working CTRL + W into muscle memory though, I've lost count of how many browser tabs I've closed by accident...
Be careful working CTRL + W into muscle memory though, I've lost count of how many browser tabs I've closed by accident...