In mathematics, the Pincherle derivative T ′ {\displaystyle T'} of a linear operator T : K [ x ] → K [ x ] {\displaystyle T:\mathbb {K} [x]\to \mathbb {K} [x]} on the vector space of polynomials in the variable x over a field K {\displaystyle \mathbb {K} } is the commutator of T {\displaystyle T} with the multiplication by x in the algebra of endomorphisms End ⁡ {\displaystyle \operatorname {End} }. Wikipedia