  In this paper we present a unified approach to establish gradient type
formulas and Bismut type formulas for backward stochastic differential
equations (BSDEs). This approach relies on a mix of derivative formulas with
respect to the conditional probability of forward SDEs and the expression of
the solution of BSDEs. Some concrete examples are given to illustrate the
results. As applications, we provide representation formulas for the control
solutions to McKean-Vlasov BSDEs and derive gradient estimates for related
PDEs.
