ln(v2/v1)
 
 
 
 
If a mathematical calculation is correct for mathematics, then it is also correct for physics.
The product rule d(f)/dt = d(gh)/dt = g dh/dt + h dg/dt is correct for mathematics, it is also correct for physics.
NO
The d(dE)/dt = d( Fdx)/dt is correct for mathematics , it is also correct for physics.
The d( Fdx)/dt = dF/dt dx + F d(dx/dt) is correct for mathematics , it is also correct for physics.
The books are wrong.
CERN