Using Exercise, prove that every polynomial belongs to C∞ (R).
Exercise
This exercise is used in Section.
a) Prove that (xn)′ = nxn−1 for every n ∈ N and every x ∈ R.
b) Prove that (xn)′ = nxn−1 for every n ∈ −N∪{0} and every x ∈ (0,∞).
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