Question regarding BTC change address and transaction

[logfiles]

I understand that  when someone is trying spend part of the BTC that is in their HD wallet. The whole amount is spent but the change gets sent back to one of the owner's wallet addresses (or in this case the change address).

Now since every BTC transaction requires a miner's fee... How is the fee of the new transaction to the change address catered for?

1. Is it part of the fee paid when spending the whole BTC amount in the first transaction or it's deducted from the change when it is being transferred to the new change address?

Thanks in advance to anyone who will help me understand these  

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[Rath_]

Now since every BTC transaction requires a miner's fee... How is the fee of the new transaction to the change address catered for?

The change is included in the same transaction; it shows as an extra output of your transaction. The transaction fee will be a little bit higher but not as much as if you were sending a separate transaction. It will be deducted from the input(s) just like the fee if there wasn't any change.

[o_e_l_e_o]

The transaction fee will be a little bit higher but not as much as if you were sending a separate transaction.

To expand on that, a 1-input-1-output transaction (for example if you are sending all the coins in a single UTXO to another address, and there will be no change left over) is in the region of 192 bytes. A 1-input-2-output transaction (the scenario described above, where whatever is not spent is sent back to you under a new address), is in the region of 226 bytes. So the additional change output will add around 34 bytes to your transaction, or even less if you are using SegWit.