Consider the function f(x) = sin (x7). a. Differentiate the Taylor series alfout 0 for f(x). b. Identify the function represented by the differentiated series. c. Give the interval of convergence of the power series for the derivative. a. Choose the correct answer below. 7x20 7x34 2! 4! OA. 7x-. OC. -7x13. + 7x27 3! 5! 7x48 6! О в. 7x6 OD. -7x' 7x20 2! b. f'(x) = c. The interval of convergence of the power series for the derivative is (Simplify your answer. Type an inequality or a compound inequality. Type an expression using x as the variable.) + 13 7x²7 3! 7x34 4! 41 7x" 5! 7x48 6! + ...

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