Restate the chain rule with the with proper hypotheses

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Reference no: EM131059407

1. Let I ⊆R be an open interval. Let c ∈ I, let n ∈ N and let f₁,....., f_n: I→R be functions. Suppose that f_i is differentiable at c for all I ∈ {1,....,n}. Prove that f₁ f₂.... F_n is differentiable at c, and find (and prove) a formula for (f₁f₂...f_n)'(c) in terms of f₁(c),....,f_n(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

Reference no: EM131059407

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