Power series for derivativesa. Differentiate the Taylor series about 0 for the following functions.b. Identify the. function represented by the differentiated series.c. Give the interval of convergence of the power series for the derivative.f(x) = e?2x

Solution 25EStep 1:Given Step 2:(a). Differentiate the Taylor series about 0 for the following functions.The general formula for the taylor series of a function centered at is Therefore for at Therefore The differentiation of the taylor series of isStep 3:(b). Identify the. function represented by the differentiated series.Therefore