  In this paper, we mainly study the derivation algebras of semi-simple Jordan
algebras over a field of characteristic $0$ and give sufficient and necessary
conditions that the derivation algebras of them are simple. As an application,
we prove that for a semi-simple Jordan algebra $J$, $TDer(Der(J)) = Der(Der(J))
= ad(Der(J))$ under some assumptions. Moreover, we also show that for a
semi-simple Jordan algebra $J$ which has a finite basis over a field of
characteristic $0$, $TDer(J) = Der(J) = Inn(J)$. This is a corollary about our
theorem which concerns Jordan algebras with unit.
