In a joint work with G. Savin, we formulate the analoge of Bernstein-Zelevinsky derivatives for the affine Hecke algebra of type A. The problem of determining the simple quotients of BZ derivatives is closely related to the quotient branching laws for p-adic general linear groups. The first part of the talk will focus on explaining constructing those simple quotients via using the derivative theory of essenially square-integrable representations. Such derivative theory is orginally developed by Jantzen and independently by Mínguez. Then I will formulate a branching law for p-adic general linear gorups, generalizing the notion of relevant pairs of Gan-Gross-Prasad, and if time permitting, I will talk about the recent progess on establishing such branching law.