  Let $X$ and $Y$ be Banach or normed linear spaces and $F\subset X$ a closed
set. We apply our recent extension theorem for vector-valued Baire one
functions arXiv:1512.03717 to obtain an extension theorem for vector-valued
functions $f\colon F\to Y$ with pre-assigned derivatives, with preservation of
differentiability (at every point where the pre-assigned derivative is actually
a derivative), preservation of continuity, preservation of (pointwise)
Lipschitz property and (for finite dimensional domain $X$) preservation of
strict differentiability and global (eventually local) Lipschitz continuity.
