Consider F and C below.

$F(x,y)=(8+8x{y}^2)i+8x^{2}yj,C$ is the arc of the hyperbola $y=\frac{1}{x}$ from $(1,1)$ to $(5,\frac{1}{5})$

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

$f(x,y)=$

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