radioactive decay equation derivation: physics

Derivation equations  for radioactive natural decay series

if a radioactive body A(say the parent) decays into a radioactive body B (say  the daughter nuclei) and B also disintegrate into another radioactive body C, in the natural decay series.

Assuming N_A is the number of atoms in body A and N_B number of atoms in body B, during a time (t)  and N₀ is the number of atoms at time t=0, and K_A is the disintegration constant of the parent nuclei while K_B , the decay constant of the daughter nuclide B.