Exact sequence of Kähler differentials

Question

In the fifth paragrph of this answer, it is claimed that $0 \to x^n \Omega^1_{R[[x]]/R} \to \Omega^1_{R[[x]]/R} \to \Omega^1_{R[[x]]/x^n / R} \to 0$ and $0 \to x^n R[x] \to R[x] \to \Omega^1_{R[[x]]/x^n / R} \to 0$ are exact. (Here $R$ denotes a field). However, it seems to me that the exact sequence, for example, the latter one should be $0 \to x^{n-1} R[x] \to R[x] \to \Omega^1_{R[[x]]/x^n / R} \to 0$.i.e. the power of $x$ in the first term should be $n-1$. I wonder if I am correct or miss something instead.