Before revision:  Afterwards, we  derive almost optimal upper bounds for ELU-neural networks in Sobolev norms up to second-order .
After revision:  Afterwards, we provide a unifying framework for the construction of approximate partitions of unity by neural networks with fairly general activation functions. This allows us to approximate localized Taylor polynomials by neural networks and make use of the Bramble-Hilbert Lemma. Based on our framework, we derive almost optimal upper bounds for ELU-neural networks in Sobolev norms up to second-order .