I think it is impossible to solve it. Your variables appear as parameters of Exp-functions, who are themselves arguments of Exp-functions. And then there are sums of them. Differentiating gives even more complicated expressions. In my opinion there is no chance to solve that.

By the way you should have posted what you have tried already, and not a .pdf - file, but Mathematica-code in order not to force people to type the expressions themselves.

ed =
  Exp[(Exp[2 b r2] - 1)/(snr (1 - a))] Exp[-2 (r1 + r2)] + 
   Exp[(Exp[2 b r1] - 1)/(snr (1 - (1 - a) Exp[2 b r1]))] Exp[-2 r1] -
    Exp[(Exp[2 b r2] - 1)/(snr (1 - a))] Exp[-2 r1] + (1 - 
     Exp[(Exp[2 b r1] - 1)/(snr (1 - (1 - a) Exp[2 b r1]))]);

D[ ed, r1] // Expand

Otherwise

res = Collect[D[ ed, r1], Exp[_]]

How would one extract e.g. r1 from this?

res[[3, 2]] // FullSimplify

Hi, yes I did. But was not possible. The error was that the system cannot be solved with the methods available to Solve.