# exponential fit error propagation

I am stuck with error propagation of exponential fit parameters:

$$y = a*e^{(b*x)}+c$$

I have available errors of fit: $$\sigma_a$$, $$\sigma_b$$, and $$\sigma_c$$

I tried to split the problem to exponential, multiplication of exponential with a, and summation with c

error of exponential: $$\sigma_{e^{(b*x)}} = e^{(b*x)} * x * \sigma_b$$ - so far so good, corresponds to the automatic solver.

when trying to make error propagation for multiplication of "a" and "$$e^{(b*x)}$$" I have the problem that it doesn't correspond to the automatic solver.

I tried: $$\sigma_{a*e^{(b*x)}}=a*e^{(b*x)} * \sqrt{(\frac{\sigma_a}{a})^2 + (\frac{\sigma_{e^{(b*x)}}}{e^{(b*x)}})^2)}$$

got stuck here and didn't continue to the summation ...

Can someone point me to the right solution please?