I'm learning about angular moment and central forces, and in my syllabus I came across this formula:

How did they get 1 over r? I am familiar with the gradient, but I've never seen the gradient calculated for a central potential, so I think I'm a little bit confused here. I would have just thought that the magnitude of $F$ equals $-d(Uc)/dr$, but apparently a factor $1/r$ comes into play, and I don't know why.

Could someone help me?

• It's a typo. The author probably meant to write $\frac{\vec{\bf r}}{r}=\hat{\bf r}$. – Qmechanic Jan 2 '17 at 21:33