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In this paper, we consider quadratic forward-backward SDEs (QFBSDEs), for{which} the drift in the forward equation does not satisfy the standardglobally Lipschitz condition and the driver of the backward system {possesses}nonlinearity of type $f(|y|)|z|^2,$ where $f$ is any locally integrablefunction. We prove both the Malliavin and classical derivative of the QFBSDEand provide representations of these processes. We study a numericalapproximation of this system in the sense of \cite{ImkDosReis} in which theauthors assume that the drift is Lipschitz and the driver of the BSDE isquadratic in the traditional sense (i.e., $f$ is a positive constant). We showthat the rate of convergence is the same as in \cite{ImkDosReis}

Differentiability of quadratic forward-backward SDEs with rough drift