I'm trying to understand a result I saw in my Chaos Theory course.
I have a vector $\vec{A}$ and I'm focusing on its $x$ component:
$$A_x = xp^2-p_x(\vec{r} . \vec{p}) - \frac{kmx}{r}$$
It is given that: $\vec{r} = r \hat{r}$.
I don't understand how the following derivative is defined:
$$\frac{\partial A_x}{\partial \vec{r}} = \hat{x}p^2-p_x\vec{p}-\frac{km}{r}\hat{x} + \frac{kmx}{r^3}\vec{r}$$
Any ideas?