  In this paper, we extend the notion of (word) derivatives and partial
derivatives due to (respectively) Brzozowski and Antimirov to tree derivatives
using already known inductive formulae of quotients.
  We define a new family of extended regular tree expressions (using negation
or intersection operators), and we show how to compute a Brzozowski-like
inductive tree automaton; the fixed point of this construction, when it exists,
is the derivative tree automaton.
  Such a deterministic tree automaton can be used to solve the membership test
efficiently: the whole structure is not necessarily computed, and the
derivative computations can be performed in parallel.
  We also show how to solve the membership test using our (Bottom-Up) partial
derivatives, without computing an automaton.
