Yes, I think that the international community responded properly, or at least as well as it could, to the Libyan coup against their terrorist dictator Gaddafi. Because although some international intervention was required after his decades of crimes, it's still a matter of self-determination, and there's only so much outsiders can do.
The international community only got involved in Libya after a coalition of Middle Eastern nations begged the UN for help. The United States and its allies used their military hardware to help the rebels only after they desperately needed help. There are two problems with this, though. One is that the rest of the Middle East didn't want to deal with Muammar Gaddafi's eccentricities. Two is that western nations and China rely on Libyan oil shipments. I feel sorry for Syria--that nation doesn't have oil fields yet Bashar al-Assad is just as obstinate as Gaddafi's regime.
Whenever the international community interferes with another country's internal affairs it is almost always a disaster. Libya however was a rare exception. Gaddafi was a crackpot dictator responsible for murder of innocents at home and abroad. When the Libyan people revolted the international community was right to support them, however they did not invade or put their own troops on the ground. They instead aided only externally, letting the Libyans take responsibility and do the majority of the actual fighting to liberate their country. This was the correct way to handle the situation.
The international community responded property to the coup against Gaddafi. NATO was correct to establish a no-fly zone to prevent Gaddafi from committing a genocide against the rebel tribes who were assembling against him. Also, the international community was correct to let the people of Libya resolve the issue of the dictator's execution by themselves.
I personally don’t really think that the international
community responded properly to the coup against Muammar Gaddafi when Libyans
tried to depose their leader. I think
that racism and hatred against Islam made some people from other countries
instantly throw their support behind the revolutionaries. Gaddafi should have received more support.