Function with differentiable partial derivates, which has non changeable second order derivates

Question

Is there a function $f:\mathbb{R}^n\to\mathbb{R},$ for which all partial derivates are differentiable, but second order derivates (of $f$) are not changeable (Hess matrix is not symetric for some $\vec{x}$)? I know that for changeability of second order derivatives sufficient condition is continuity of second order derivatives (which is stronger than differentiability of partial derivatives). Only existency of sec. or. derivatives is however not sufficient.