For each of the following, decide if the given vector field is a gradient of a function f. If so, give find the function f and enter it as your answer; if not, enter the word none for your answer and be sure that you are able to explain why this is the case. (a) [8xcos(x^2 + y^2)]i + [8y cos(x^2 + y^2)]j:f = (b) [4xy]i + [4xy]j:f = (c) [8cos(x^2 + 8y^2) - 16x^2 sin(x^2 + 8y^2)]i + [-128xy sin(x^2 + 8y^2))]j:f = (d) [6xy]i + [3x^2]j:f =