Note on certain formulae in the calculus of operations. (Q1556109)

Die Formeln, welche in Prof. Tait's oben erwähnter Arbeit vorkommen, sind: \[ \left( \frac{d}{dx} x\;\frac{d}{dx} \right)^{n} = \left( \frac{d}{dx} \right)^{n} x^{n} \left( \frac{d}{dx} \right)^{n}, \] \[ \left(x\;\frac{d}{dx}\;x \right)^{n} = x^{n} \left(\frac{d}{dx} \right)^{n} x^{n}. \]