Gradient wrt. a Position Vector

I found the following equations in a dynamics textbook,

The gravitational potential energy for any two particles in a $n$-particle system is given by,

$$V_{ij} = – frac {G m_i m_j}{r_{ij}}$$

where $r_{ij}$ is the distance between $m_i$ and $m_j$. The total potential energy of the system is,

$$V = frac{1}{2} sum_{i = 1}^{n} sum_{j = 1}^{n}V_{ij} qquad (i neq j)$$

If $R_i$ is the postion vector of the $i^{th}$ particle, then

$$frac{partial{V}} {partial {vec{R_{i}}}} = – frac{partial{V}}{partial{vec{r_{ji}}}} + frac{partial{V}}{partial{vec{r_{ij}}}} = -2 frac{partial{V}}{partial{vec{r_{ij}}}}.$$

What does it mean to take the derivative of a Scalar Function$(V)$ with respect to a vector$(vec{R_1})$? Is it directional derivative?

I’ve been trying all day to get the last equation. I would be very grateful if somebody could help me(or mention some reference perhaps). I don’t really know which part of math is used to get the last equation.