How can I make a palm tree sway?

How can I make a palm tree sway?

I have a palm tree that is a tiff file with alpha. I would like the tree trunk to bend a little and a few of the branches to sway as though it’s gently moving in the wind.

What would be the easiest way to make that happen?

Should I save the trunk and a few leaves as separate elements, and then animate them in motion.

Or is there any way to turn my palm tree into a shape in motion, add edit points and key frames to animate it?

Any advice would be appreciated.

Thanks