Show, by finding a potential V(r) such that F = −∇V , that F is conservative

Question

A particle at position r experiences a force:

$$F=(-\frac{a}{r^2}+\frac{b}{r^3})\hat{r}$$

a and b are constants and $\hat{r}$ is the unit vector in a radial direction. I am told that I will need the fact that ∇r = $\hat{r}$.

I really don't know where to get started finding V

Answer 1

By the symmetry of $F$, $V$ will be radial: $V({\bf r})=f(r)$ for some $f:{\Bbb R}\longrightarrow{\Bbb R}$. Using the chain rule, $\nabla V=...$?