Problem 743 (difficulty: 5/10)

Assume that \(\displaystyle f\) and \(\displaystyle g\) are \(\displaystyle n\) times differentiable at the point \(\displaystyle a\).

(a) Prove that \(\displaystyle fg\) is also \(\displaystyle n\) times differentiable at the point \(\displaystyle a\).

(b) \(\displaystyle (fg)^{(n)}(a)=?\)

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