Prove polynomial ring over a discrete valuation ring quotient by powers of maximal ideal is regular?

Question

Let $(R,\mathfrak{m},k)$ be a discrete valuation ring, (of characteristic $p$ if you need).

Let $n\geq 1$ be an integer.

Is the ring $\frac{R}{\mathfrak{m}^n}[x]$ regular?

Note that: Regularity can be checked at localisation of maximal ideals.