Classical Dynamics of Particles and Systems · Problem 1-28

This is about understanding how gradients work on scalar functions of position. The key insight is that $\ln|\mathbf{r}|$ depends only on the distance $r$ from the origin, so you can use the chain rule: take the derivative with respect to $r$, then multiply by $\nabla r$. Once you find $\nabla r = \frac{\mathbf{r}}{r}$, the rest follows naturally from the chain rule applied to a radial function.

This is about understanding how gradients work on scalar functions of position. The key insight is that $\ln|\mathbf{r}|$ depends only on the distance $r$ from the origin, so you can use the chain rule: take the derivative with respect to $r$, then multiply by $\nabla r$. Once you find $\nabla r = \frac{\mathbf{r}}{r}$, the rest follows naturally from the chain rule applied to a radial function.