marginal laws of $(Y,Z)$ in [@ab; @ak; @mpr]. However, in all the above references, the authors always refer to either [@pardouxpeng; @EPQ] in a Lipschitz context or [@ank] in a quadratic context, when stating differentiability results in the Malliavin sense (see for instance the sentence before Theorem 2.2 in [@ak], or Step 2 in the proof of Theorem 3.3 in [@ab], which refers to [@ak], or the proof of Part a) of Theorem 2.6 in [@hns], or Proposition 3.2 in [@mpr]).

The aim of this paper is to provide an alternative sufficient condition to (EPQ1)-(EPQ2) for the Malliavin differentiability of the solution to a BSDE of the form in the general non-Markovian setting. Our main result in that direction is Theorem \[thm:yzd12\] below, using a fundamentally different approach from [@EPQ; @pardouxpeng], as well as different type of assumptions. Since they involve some notations concerning the analysis on the Wiener space, we refrain from detailing them immediately, and rather explain informally what are the main differences between our approach and the one of [@EPQ]. A natural way to solve a BSDE of the form when the driver $f$ is Lipschitz in $(y,z)$ is to make use of a Picard iteration, that 