Consider the vector field vec$(F)$ and the curve $C$ below.

vec$(F)(x,y)=(74x{y}^2)i4x^{2}yj$

$C$ is the arc of the hyperbola $y=\frac{1}{x}$ from $(1,1)$ to $(3,\frac{1}{3})$

$($a$)$ Find a potential function $f$ such that vec$(F)=$gradf.

$f(x,y)=$

$($b$)$ Use part $($a$)$ to evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$gradf$*dr$ along the given curve $C.$