Newly planted dwarf burning bush.
 

I just planted a dwarf burning brush and noticed some of the leaves yellowing and dying. Any thoughts?

Trim off the dead/dying branches. You can literally cut those bushes down to the stump and they will grow back. But you don't want it wasting nutrients and energy trying to save dying branches.
Make sure to water thoroughly and regularly for first couple of weeks (but don't drown it, so check the soil and keep moist but not wet).

Also, add in little starter fertilizer or Miracle-Gro granules, mixed into soil at the base, and 2-3" of mulch.

I have been watering thoroughly in the mornings as I'm in southeastern Ohio and been around 90 and up with humidity. I used some Miracle Grow all purpose plant food for trees, shrubs, flowers, etc.
I will cut off the dead sections and try to better monitor moisture of soil.

Thx. Mike

That kind of weather makes it tough but you might be able to save it with that plan