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while not an exact duplicate, the logic of deriving keys is mentioned in this thread: https://bitcoin.stackexchange.com/questions/69315/how-are-compressed-pubkeys-generated/69322?noredirect=1#comment80498_69322. When having a private key, you can load it into bitcoind with "importprivkey", explanations in the API calls list (https://en.bitcoin.it/wiki/Original_Bitcoin_client/API_calls_list). I hadn't found a direct way to see, which address belongs to a private key, but a "getaddressesbyaccount" before and afterwards did the trick for me.

and a second link: https://bitcoin.stackexchange.com/questions/1389/how-are-public-private-keys-in-an-address-created/1715#1715 - if this is not sufficient, maybe you can outline your question a bit more, so we can understand, what tool(s) you would like to use? There is python, Java, shell scripts, ...