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State and prove a theorem that gives a formula for $f′(x_0)$ when $f = f_n\circ f_{n−1}\circ\cdots\circ f_2\circ f_1.$ (Be sure to state all the hypotheses that you need.)

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    This sounds like something dumped here from a set of exercises. A better idea is to tell us why this problem interests you, what you have been able to do with it, where you get stuck, and so on.2012-11-01
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    As Cameron Buie mentions, this is essentially an iterated chain rule. I would try induction.2012-11-01

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