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) $[ 6 y ]\,\vec i + [ 7 x ]\,\vec j$: $f =$

(b) $[ 8 x y ]\,\vec i + [ 4 x^2 ]\,\vec j$: $f =$

(c) $[ 6 x\cos(x^2 + y^2) ]\,\vec i + [ 6 y\cos(x^2 + y^2) ]\,\vec j$: $f =$

(d) $[ 2\cos(x^2 + 2 y^2) - 4 x^2\sin(x^2 + 2 y^2) ]\,\vec i + [ -8 x y\sin(x^2 + 2 y^2) ]\,\vec j$: $f =$