  Let $B_t$ be a one dimensional Brownian motion, and let $\alpha'$ denote the
derivative of the intersection local time of $B_t$ as defined in Jay Rosen's
work (see references). The object of this paper is to prove the following
formula $(1/2)\alpha'_t(x) + (1/2)sgn(x)t = \int_0^t L_s^{B_s - x}dB_s -
\int_0^t sgn(B_t - B_u - x) du$ which was given as a formal identity by Rosen
without proof.
