  In this paper, we study higher derivations of Jacobian type in positive
characteristic. We give a necessary and sufficient condition for $(n-1)$-tuples
of polynomials to be extendable in the polynomial ring in $n$ variables over an
integral domain $R$ of positive characteristic. In particular, we give
characterizations of variables and univariate polynomials by using the terms of
higher derivations of Jacobian type in the polynomial ring in two variables
over a field of positive characteristic.
