- #1

- 12

- 0

I'm trying to take the gradient of the potential function, and know the answer, but am not sure how to go about it. Can someone help me step by step as to how to do this.

So the potential function is:

\begin{equation}

U = \frac{1}{2} G \sum^{N}_{i=1} \sum^{N}_{j=1,j \neq i} \frac{m_i m_j}{\| \mathbf{r}_{ji} \|}

\end{equation}

Now I'm trying to take the gradient or partial with respect to $$\mathbf{r}_i$$

\begin{equation}

\frac{\partial U}{\partial \mathbf{r}_i} = -G \sum^{N}_{j=1,j \neq i} \frac{m_i m_j}{\| \mathbf{r}_{ji} \|^3} \mathbf{r}_{ji}

\end{equation}

So my question is, how do you go from the first equation to the answer (the second equation). If you could explain step by step with math that'd be appreciated. Thanks!