Deriving the curl of the magnetic field

[pkjag]

So i was wondering how the curl of the magnetic field is derived since Feynman just introduces it from nothing in his second volume of Feynman's lectures on physics:

c²∇xB=j/ε₀

or the other one where ∇x B=μ₀j

 

[dextercioby]

Do you know about the Biot-Savart's law and how to pass mathematically from one type of integral to another (Stokes formulas) ?