  We consider Backward Stochastic Differential Equations (BSDE) with generators
that grow quadratically in the control variable. In a more abstract setting, we
first allow both the terminal condition and the generator to depend on a vector
parameter $x$. We give sufficient conditions for the solution pair of the BSDE
to be differentiable in $x$. These results can be applied to systems of
forward-backward SDE. If the terminal condition of the BSDE is given by a
sufficiently smooth function of the terminal value of a forward SDE, then its
solution pair is differentiable with respect to the initial vector of the
forward equation. Finally we prove sufficient conditions for solutions of
quadratic BSDE to be differentiable in the variational sense (Malliavin
differentiable).
