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Based on Lions \\cite{Lions}, Cardaliaguet \\cite{Cardaliaguet} (Theorem 6.2 and 6.5) proved that: \\bea \\label{Derivative} D F (\\xi) = g(\\xi), \\eea where $g: \\mathbb{R} \\to \\mathbb{R}$ is a deterministic function which depends only on the law of $\\xi$. See also Carmona \\& Delarue \\cite{CD} Section 5.2. In this short note we provide an elementary proof for this well known result. 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