JavaCard OS

My card needs to implement the mutual authentication.

For that purpose the outside card application and the card must share the set of secret keys. The first key is relevant for encryption and the other for the MAC calculation. At this point I am putting these keys on the card during the personalization.

Now my question is if it's secure enough. I read that it is recommended to use derived keys such that only one card is affected if a key is compromised. How can I calculate the derived keys?

Derived keys are considered more secure. As you said, if the keys for one card is compromised some how, only that card is affected.

If you have the space and want more secure, you can use a completely random key for card.