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 (fgh)ʹ(a) = f'{a)g{a)h{a) + f{a)g'{a)h{a) + f(a)g(a)h'(a).
b) II f is differentiable at a and g is differentiable at f(a), then (8 o f)ʹʹ = gʹf(a))f"{a) + 8"(f(a))(f'(a))2.
c) If the nth-order derivatives f(n){a) and g(n){a) exist, then (f + g)(n)(a) = f(n)(a) + g{n)(a).
d) If the nth-order derivatives f(n)(a) and g(n)(a) exist and are nonzero, then

g(a)f(a) +(-1)" f(a)g(a) gtl(a)