The common theorem about the points of discontinuity of mappings  $f: X × Y → Z$ which are quasicontinuous with respect to the first variable and have the Lipschitz property at every point with respect to the second variable is given. It is shown that the set of discontinuity of every separately differentiable function  $f: \mathbb{R}^n → \mathbb{R}$ is nowhere dense in $\mathbb{R}^n$ and on every hiperplane  $x_i = const$. 

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