Let $Q$ be a delta endomorphism. There exists a unique shift-invariant and invertible endomorphism $U$ such that $Q = D \circ U$. We denote by $(q_n)_{n \in \mathbb{N}}$ the sequence of polynomials associated with $Q$.
Prove that, for all $n \in \mathbb{N}^*$, we have
$$\left(Q' \circ U^{-n-1}\right)\left(X^n\right) = X U^{-n}\left(X^{n-1}\right)$$