Forward Difference of Falling Factorial

Theorem
Let $$f: \R \to \R$$ be a real function.

Let $$\Delta$$ be the forward difference operator.

Let $$x^{\underline m}$$ be the $m$th falling factorial of $$x$$

Then:
 * $$\Delta \left({x^{\underline m}}\right) = m x^{\underline{m-1}}$$

Proof
From the definitions:

$$ $$ $$ $$ $$ $$