fungus on tree
The picture shows a fungus in the genus Hericium. These are bracket fungi called lion's mane or tooth fungus, due to those spines that project downward. They are common on trees in wet weather, in the late summer and fall, particularly on beech trees. They are a sign that a fungus has colonized that part of the tree, but will not kill the tree. These fungi are actually prized edibles, but I do recommend that people do not eat fungi they collect in the woods unless they absolutely have it identified in person by an expert. These Hericium species are pretty unmistakable though.
I would prune off that dead branch, but I do not believe it will kill the tree. Thank you so much for sending in this picture, it is a beautiful fungus! Thank you too for contacting Delaware Cooperative Extension.