Suppose that I is an open interval containing a, and that f, g, h : I → R. Decide which of...

Suppose that I is an open interval containing a, and that f, g, h : I → R. Decide which of the following statements are true and which are false. Prove the true ones and provide counterexamples for the false ones.

a) If f, g, and h are differentiable at a, then

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b) If f is differentiable at a and g is differentiable at f (a), then

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c) If the nth-order derivatives f (n)(a) and g(n)(a) exist, then

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d) If the nth-order derivatives f (n)(a) and g(n)(a) exist and are nonzero, then