  We consider a multidimensional SDE with a Gaussian noise and a drift vector
being a vector function of bounded variation. We prove the existence of
generalized derivative of the solution with respect to the initial conditions
and represent the derivative as a solution of a linear SDE with coefficients
depending on the initial process. The representation obtained is a natural
generalization of the expression for the derivative in the smooth case. The
theory of continuous additive functionals is used.
