  Let X_t be a subordinate Brownian motion, and suppose that the Levy measure
of the underlying subordinator has completely monotone density. Under very mild
conditions, we find integral formulae for the tail distribution P(\tau_x > t)
of first passage times \tau_x through a barrier at x > 0, and its derivatives
in t. As a corollary, we examine the asymptotic behaviour of P(\tau_x > t) and
its t-derivatives, either as t goes to infinity or x goes to 0.
