When you are logged into webmail on your University of Derby account you can sign out of this account and log into a different Office 365 account.
Please Note: If you try and select sign out when you are in the mail app it might not sign you out - so go to 'Office 365' then sign out:
If you are in webmail (https://outlook.office.com/mail/inbox)
1. Click on 'Office 365' in the top left of the screen;
2. Click on your profile picture in the top right and select Sign out;
3. You will then see a page that confirms you have logged out of your account;
4. Click Switch to a different account which will show a text box, enter the email address of your other account into here;
5. Click the Sign in button;
6. If you are signing into your university account, the site will re-direct to a log in page, enter your credentials and select sign in, otherwise Office 365 will log you into your other account.