Spending transaction output with only xpriv key

Question

Is it possible to spend a P2WPKH transaction output, with only knowing the xpriv key and not knowing the specific private key that corresponds to the public key of the transaction?

Answer 1

No, you need the private key that the address in question was derived from.

There is no mechanism for the wider network to determine that an address was derived from a private key, that was derived from a specific xpriv. The transaction signature must be created using the private key that is related to the address in question.

Answer 2

The extended private key (xprv) can derive all the individual WIF private keys associated with that HD account. So technically it is possible to parse through the xprv keychain until you find the individual WIF private key that corresponds with the output you want to spend from.

For example, if you know the output address you want to spend from you could write a script that loops through each private key.

Psuedo code:

var myxprv = "xprv1234....";
var outputaddr = "bc1wqSomeAddress....";
var notfound = true;
var index = 0; 

while(notfound){
    var eachPK = fromXprv(myxprv,0,index);
    var details = wif2Address(eachPK);
    if(outputaddr===details.p2wpkh){
        notfound = false;
        return "found";
    } else {
        index++;
    }
}