Differentiate the given series expansion of f term-by-term to obtain the corresponding series expansion for the derivative of f . f(x) = 1 + 4x ( - 1)74 x f'(x) = n=1Integrate the given series expansion of f term-by-term from zero to x to obtain the corresponding series expansion for the indefinite integral of f. 82 7 f(x) = ( - 1)"8x-8 +7 1 +x8 7=0 f(t)dt = 0 n=0