Let us consider two points A and B lying very near to each other at a distance \( dr \) in a gravitational field \( E \) acting in the direction from B to A as shown in the adjoining fig.

Let the potential at A is \( v \) and at B is \( v+dv \). The work done in moving a unit mass from B to A along the direction of force is

\begin{split}
E\cdot{dr}&=v - (v+dv)
\\E\cdot{dr}&=-dv
\\E&=-\frac{dv}{dr}
\end{split}