Many people make the mistake of holding the trombone slide too hard. Usually, they grip it with a claw-like handgrip, with too much pressure and tension. The right wrist should remain loose to bend freely when you move the slide. Think of how flexible your wrist is when you bounce a ball up and down, ready to softly catch and slide the ball back down with a wrist arch. This is the same looseness that you should feel when playing the slide. You will find it much easier to move the slide faster and with better fluidity if you keep your wrist loose.