7. Complete the table of derivatives for f (x) = sin (x )cos (x) (use technology to help find the derivatives). Write out the first few non-zero terms of the series to help you find a pattern, then write the Maclaurin series in Y a,x\"* form using a starting index of n = 0. (7 points) 0 5 1 6 2 7 3 8 4 9 First few terms: Series: 8. Consider the function f(x)= %x3s'1n(2x) . (5 points) a. Determine the Taylor series for the function using Theorem 8.8.2. Show relevant steps. Write your final simplified answer in the form X a,x\"*. b. Determine the Taylor series for f '(x) and its interval of convergence. 9. (Multiple Choice) The interval of convergence of the Maclaurin series for tan\"' ( 2x) is: (1 point) A. [-1,1] B. [2,2] C. 11 _E;E] D. (o0,)