Would the United States Defend Japan if say North Korea or China attacked them?

while i know for a fact the JSDF is small and not as 'big budgeted' as most military forces are. the Japanese Maritime Defense Force (JMSDF) is more than capable of defeating the Chinese and Korean navy because the Japs use much more modernized ships and are trained by the US Navy not to mention the Japanese air force could hold its own against their air forces because they use F-15's F-16's F/A-18's ect but i was just wondering in case of an attack made by a country twards japan how would the US respond? i know we have several bases in the mainland japan and in Okinawa theirs even been some controversy regarding the US building ICBM instillations on Okinawa and Japan is also one of our closest allies and is a major economical partner. so Japan is definitely a very important little Island to the US.