A. Differentiate the Taylor series about 0 for the function f (x )equalse Superscript 2 x. b. Identify the function represented by the differentiated series. c. Give the interval of convergence of the power series for the derivative. a. Which of the following is the derivative of the Taylor series about xequals0? A. 2 Summation from k equals 1 to infinity StartFraction x Superscript k Baseline minus 1 Over (k minus 1 )exclamation mark EndFraction B. Summation from k equals 0 to infinity StartFraction x Superscript k minus 1 Over (k minus 1 )exclamation mark EndFraction C. Summation from k equals 1 to infinity StartFraction (2 )Superscript k Baseline x Superscript k minus 1 Over (k minus 1 )exclamation mark EndFraction D. 2 Summation from k equals 0 to infinity StartFraction x Superscript k minus 1 Over (k minus 1 )exclamation mark EndFraction b. What is the function represented by the differentiated series? f (x )equals nothing c. What is the interval of convergence? nothingless thanxless than nothing