So, i have a dataset which behaviour could be approached by the power law:

$ $ N(x)= a – bx^{-1/c} $ $

So i am doing this to get the regression:

nlm = NonlinearModelFit[data, a - b*x^(-1/c), {{a, 0}, {b, 0}, {c,2}}, x, MaxIterations -> \[Infinity]] 

So i get the following result:

Then i get these standard deviations for a, b, c:

Now i am using the gaussian law for error propagation to calculate the standard deviation of N(x):

\[Sqrt]((D[a - b*x^(-1/c), a]*11426.108699236138`)^2 + (D[a - b*x^(-1/c), b]*1.434690881054167`*^8)^2 + (D[a - b*x^(-1/c),c]*0.03626373539623972`)^2)  a = 3.2763042912759576`*^6; b = 1.4018942844796562`*^9; c = 2.320026692762461`; 

Then i am getting the resulting function:

When i plot the resulting function sigma N(x), i am getting this graph:

So the error term is declines for x going to infinity.

Now my goal is to get the standard deviation for:

$ $ N(x) \rightarrow \infty $ $

So i have done this:

So i am not that experienced in error calculations, and i am not sure if my action was right. I would be thankful if somebody could have a look on it.