Per the rules for mounted combat:
The initiative of a controlled mount changes to match yours when you mount it. It moves as you direct it, and it has only three action options: Dash, Disengage, and Dodge. A controlled mount can move and act even on the turn that you mount it.
and
if the mount provokes an opportunity attack while you’re on it, the attacker can target you or the mount.
If a controlled mount takes the Disengage action and moves away from an enemy, does the rider still provoke an attack of opportunity attack if he or she does not also take the Disengage action? In other words, can I ride up to an enemy, make a melee attack, then have my mount disengage and ride away, without provoking an opportunity attack?