Theorem 6.11 (Leibniz's Rule).  Let G be an open set,  and let    be an interval of real numbers.  Let and its partial derivative with respect to z be continuous functions for all z in G and all t in I.  Then  

               is analytic for z in G, and  

            .  

Demonstration for Theorem 6.11.

(c) 2006 John H. Mathews, Russell W. Howell