Here I show how to derive the explicit presentation of the momentum operator $\hat p$ in $x$-space: $\hat p = -\mathrm{i}\frac{d}{dx}$ out of the commutation relation $[\hat x, \hat p]=\mathrm{i}$. I wonder, why all textbooks on quantum mechanics omit this issue. This fact is implicitly kept in mind but never is presented explicitly. The prove of this fact is simple.
