  By employing consistent supersymmetric higher derivative terms, we show that
the supersymmetric theories may have a sector where the scalar potential does
no longer have the conventional form.
  The theories under consideration contain consistent higher-derivative terms
which do not give rise to instabilities and ghost states. The chiral
auxiliaries are still not propagating and can be integrated out. Their
elimination gives rise to emerging potentials even when there is not a
superpotential to start with. This novel feature of higher derivative
supersymmetric chiral models is also extended to vector multiplets both in
global and local supersymmetry. In particular, in supergravity, the emerging
potentials give rise always to a de Sitter vacuum signaling supersymmetry
breaking.
