Solve an equation involving partial derivative?

Questions
1

I am looking for someone who can solve an equation using Mathematica. The equation needs the process of doing partial derivative. The issue is the equation is complicated and hence cannot be solved by the methods that I have tried.

mathematica1.pdf (150 KB)

2

Hi Karthi,

Have you tried using Solve?

3

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

4

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