Since recognizable tree languages are closed under the rational operations, every regular tree expression denotes a recognizable
tree language. We provide an alternative proof to this fact that results in smaller tree automata. To this aim, we transfer
Antimirov’s partial derivatives from regular word expressions to regular tree expressions. For an analysis of the size of
the resulting automaton as well as for algorithmic improvements, we also transfer the methods of Champarnaud and Ziadi from
words to trees.