1. Let I ⊆R be an open interval. Let c ∈ I, let n ∈ N and let f1,....., fn: I→R be functions. Suppose that fi is differentiable at c for all I ∈ {1,....,n}. Prove that f1 f2.... Fn is differentiable at c, and find (and prove) a formula for (f1f2...fn)'(c) in terms of f1(c),....,fn(c) and f'1(c),...., f'n(c).
2. Let I ⊆R be an open interval. Let c ∈ I, let f, g:I→R be functions and let k ∈ R. Suppose that f and g are differentiable at c. Prove kf is differentiable at c and |kf|'(c) = kf'(c).
3. Explain the flaw in the proof in the attachment. Restate the Chain Rule with the proper with modified hypotheses that would make the attempted proof into a valid proof.
Attachment:- attachment.rar