Question: 7. Suppose that f, a function analytic in an open set U. is a member of the class C?(U), the functions with 2 continuous derivatives.

7. Suppose that f, a function analytic in an open set U. is a member of the class C?(U), the functions with 2 continuous derivatives. Demonstrate that its derivative f' is then analytic in U. Conclude that a function f which is analytic in U and also belongs to the class Co (U) which are functions with continuous derivatives f', f", f", ... of all orders in U

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