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) = sin(x2)

Solution 24EStep 1:In this problem we have to find the power series for derivatives.a. Differentiate the Taylor series about 0 for the following functions.We have The taylor series for with center 0 is Differentiate, we get Step 2:b. Identify the function represented by the differentiated series.The differentiated series is which is Therefore the function represented by the differentiated series of is .