Simplifying a differential equation

[mash17]

When I multiply out the first line I end up with an extra (dA/dx)*(dσ/dx). Can someone please show me how i get from the first line to the second. Thanks

 

[Bill_K]

The extra term is dA/dx · dσ/dx · dx · dx, which can be dropped because dx is an infinitesimal quantity and this term is second order in dx, infinitesimally smaller than the term you keep, which is first order.