Problem with deriving a standard deviation function

Question

I have a function which depicts errors for a specific parameter. The function for the standard deviation of this parameter is also given, but I am having problems deriving it from the error function. The error function is the following: $$ \epsilon_f = C\sum_{m=1}^{M}\sum_{n=1}^{N}\nu_m\mu_nR(\alpha_m)\epsilon_g(\alpha_m,\beta_n) $$ Here C is a constant. The original function is an integral which has been discretized. It is assumed that the noise in $g$ is zero mean white Gaussian and homogeneous, so that the noise can be described only by its standard deviation. Thus, the function for the standard deviation of $f$ is shown to be $$ \sigma_f =\sigma_gC\sqrt{\sum_{m=1}^N\mu_n^2\sum_{n=1}^N(\nu_mR_m)^2} $$ Now, I've been unable to use this function correctly, so I've tried to derive the function myself to see if there is something 'hidden'. But I can't quite see how the equation is obtained. I am not necessarily looking for a complete step-by-step answer, if somebody could show me the correct path I would appreciate it.