Question

what is the derivation for Newton's law of motion

Answer 1

Do you want basic derivation of calculus approach ?

Answer 2

http://en.wikipedia.org/wiki/Newton's_laws_of_motion

Answer 3

@ trsram yes

Answer 4

the second law's derivation is............
"force is proportional to the rate of change of momentum"
F=dP/dt
=d(mv)/dt
=m(dv/dt)
=ma(since dv/dt=velocity v)
hence F=ma

Answer 5

For an even more general derivation, you'll need to get familiar with Lagrangians and the Principle of Least Action.