Let f(x) =x sin x and g(x) =x cos x. (a) Show that f'(x) = g(x) + sinx and g'(x) = -f(x) + cos x. (b) Verify that f"(x) = – f(x)+2 cos x and g"(x) = -8(x) – 2 sin x. (c) By further experimentation, try to find formulas for all higher deriva- tives of f and g. Hint: The kth derivative depends on whether k = 4n, 4n + 1,4n + 2, ог 4n + 3.

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