Show the equality: for all $m \geq 0$ and $\mu \geq 0$,
$$\left(\frac{d}{dx}\right)^{\mu} \cdot \left(x^m f\right) = \left(x^m \left(\frac{d}{dx}\right)^{\mu} + \sum_{i=1}^{\min(\mu,m)} \frac{m(m-1)\cdots(m-i+1)\,\mu(\mu-1)\cdots(\mu-i+1)}{i!} x^{m-i} \left(\frac{d}{dx}\right)^{\mu-i}\right) \cdot f.$$