How to send my 2X coins to an exchange from a private BTC wallet I had during the fork?
The 2x fork did not activate (there was a fatal bug in the code, perhaps more than one), so there is no 2x network on which to send coins.

On some exchanges, people are trading financial contracts issued by the exchange, which are related to the expected outcome of the 2x hard fork situation. This is different from an actual 2x coin (which does not exist).