The drywall around a corner of a support beam in the house cracked and broke off of it. It's not big but I can see metal. I was wondering if I could just smear drywall compound onto to fix it, or is there a more proper method?

We have a leak that has caused water to leak behind a window seal. I was trying to remove the paint and chunks of dry wall came with it. I need to know how to repair it myself.