If $T$ is an endomorphism of $\mathbb{K}[X]$, its Pincherle derivative $T'$ is defined by $$\forall p \in \mathbb{K}[X], \quad T'(p) = T(Xp) - XT(p)$$ If $T$ is a delta endomorphism, show that $T'$ is a shift-invariant and invertible endomorphism.
If $T$ is an endomorphism of $\mathbb{K}[X]$, its Pincherle derivative $T'$ is defined by
$$\forall p \in \mathbb{K}[X], \quad T'(p) = T(Xp) - XT(p)$$
If $T$ is a delta endomorphism, show that $T'$ is a shift-invariant and invertible endomorphism.