  We comment on a Mazur problem from "Scottish Book" concerning second partial
derivatives. It is proved that, if a function $f(x,y)$ of real variables
defined on a rectangle has continuous derivative with respect to $y$ and for
almost all $y$ the function $\,F_y(x):=f'_y(x,y)$ has finite variation, then
almost everywhere on the rectangle there exists the partial derivative
$f"_{yx}$. We construct a separately twice differentiable function, whose
partial derivative $f'_x$ is discontinuous with respect to the second variable
on a set of positive measure. This solves in the negative the Mazur problem.
