Generalised Lorentz force expression from Classical Mechanics by Goldstein

I am reading chapter 7 in the 3rd edition of Goldstein’s Classical mechanics textbook and the expression for the Lorentz force is confusing me. I cannot scan it so I am just going to write it out verbatim and formulate my question afterwards. Here is the extract of page 298 from the text:

In terms of $phi$ and $mathbf{A}$, the Lorentz force is $$mathbf{F} = q{-nablaphi+frac{1}{c}frac{partial mathbf{A}}{partial t} + 1[v times(nablatimes mathbf{A})]}tag{7.67c}.$$
This suggests that we should generalize the force law to
$$frac{dp_{mu}}{dtau} = qleft(frac{partial (u^nu A_nu)}{partial x^mu}-frac{dA_mu}{dtau}right).tag{7.68}$$

The first equation is the three three dimensional Lorentz force express using the vector and scalar potentials (As a note I think the second term should be $-frac{partial A}{partial t}$ but the above is as written.)

I am unsure howhow you reach the second equation from the first expression, I would appreciate any help in understanding this problem.