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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4$\begingroup$ 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. $\endgroup$– Gerry MyersonCommented Nov 1, 2012 at 4:44
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$\begingroup$ As Cameron Buie mentions, this is essentially an iterated chain rule. I would try induction. $\endgroup$– EuYuCommented Nov 1, 2012 at 4:56
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1 Answer
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Hint: This is a generalization of chain rule, and works basically the same way.
answered Nov 1, 2012 at 4:50