Exercise 4.3.2. Let I CR be an open interval, let c E I, let n E N and let fi,..., fn : I–R be functions. Suppose that fi is differentiable at c for all i E {1,...,n}. Prove that fi f2 -. fn is...

4.3.2

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Extracted text: Exercise 4.3.2. Let I CR be an open interval, let c E I, let n E N and let fi,..., fn : I–R be functions. Suppose that fi is differentiable at c for all i E {1,...,n}. Prove that fi f2 -. fn is differentiable at c, and find (and prove) a formula for (fi f2·… fn)' (c) in terms of fi (c), ..., fn(c) and f{(c),..., f„(c).