  In the 60's Levine proved that if $R$ is a slice knot, then on any genus $g$
Seifert surface for $R$ there is a $g$ component link $J$, called a derivative
of $R$, on which the Seifert form vanishes. Many subsequent obstructions to $R$
being slice are given in terms of slice obstructions of $J$. Many of these
obstructions can be derived from a 4-manifold called a null-bordism. Recently
the authors proved that that it is possible for $R$ to be slice without $J$
being slice, disproving a conjecture of Kauffmann from the 80's. In this paper
we cut open these null-bordisms in order to derive new obstructions to being
the derivative of a slice knot. As a proof of the strength of this approach we
re-derive a signature condition due to Daryl Cooper. Our results also apply to
doubling operators, giving new evidence for their weak injectivity. We close
with a new sufficient condition for a genus 1 algebraically slice knot to be
$1.5$-solvable.
