Any way to prove this identity :$\frac{d^m}{dx^m}\frac{H(x)x^{m-1}}{(m-1)!} =\delta(x)$?

Question

One of my friend sent me to proof this identity :$\frac{d^m}{dx^m}\frac{H(x)x^{m-1}}{(m-1)!} =\delta(x)$ Where $\delta$ is the dirac delta function and $H$ is heaviside step function , I knwo only that derivative of the first order of heaviside step function present dirac function, But i never saw the titled formula with $m$ th derivative , Then does the title identity a well known formula ? and how i can show it ?