I need to hook up an out door faucet that is over 40 ft away from the nearest 3/4" pipe. Should I use 3/4" copper pipe to the faucet or will 1/2 inch suffice?

A !/2" branch off a 3/4" main should give you plenty of pressure at the end of a 40 foot run providing it isn't a up hill run, however some local codes mandate running 3/4 to a hose bib. Check your local codes to be sure. Good luck, Tom