Let (x) = x sin x and g(x) = x cos x. (a) Show that (x) =
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Let ƒ(x) = x sin x and g(x) = x cos x.
(a) Show that ƒ(x) = g(x) + sin x and g'(x) = −ƒ(x) + cos x.
(b) Verify that ƒ'(x) = −ƒ(x) + 2 cos x and g'(x) = −g(x) − 2 sin x.
(c) By further experimentation, try to find formulas for all higher derivatives of ƒ and g. The kth derivative depends on whether k = 4n, 4n + 1, 4n + 2, or 4n + 3.
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Let fx x sin x and gx x cos x a We examine first derivatives fx sin x x cos x ...View the full answer
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