Question: Consider the function f(x) = sin x, where is a constant. (a) Find the first-, second-, third-, and fourth-order derivatives of the function. (b) Verify

Consider the function f(x) = sin x, where is a constant.

(a) Find the first-, second-, third-, and fourth-order derivatives of the function.

(b) Verify that the function and its second derivative satisfy the equation f ″(x) + 2 f(x) = 0.

(c) Use the results of part (a) to write general rules for the even- and odd-order derivatives f (2k) (x) and f (2k−1) (x).

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