The first thing you should do is look into the different types of equilibrium that exist. What you have stated above is one of the “3" standard equilibrium cases.
If you want to try to derive the equations yourself, then start at the beginning. You know that at the beginning, you only have A available, so any amount of B is formed from the decay of A. You can then write out the amount of B formed at time t is given by the amount of A that decays. So the amount of B formed is, –dN(A)/dt = N(t)*lamda(A). But then you have the added complication that B is also decaying. So the rate of decay of B is dN(B)/dt = N(t)*lamda(A) - N(t)*lamda(B), or the production of B, minus the amount lost through decay.
That is not the full answer, but it is a start.