Error propagation

I have a question regarding finding the error associated with the $r\_\mathrm e$ term in the equation


$$r\_\mathrm e=\sqrt{\frac h{8\tilde B\_\mathrm e\pi^2\tilde c\mu}}$$


Is there anyway I can find the uncertainty of $r\_\mathrm e$ using any formula. $h$, $\pi$ and $\tilde c$ and $\mu$ all are constant. Only $\tilde B\_\mathrm e$ have an uncertainty. Any readings that I could tap into?




If the individual uncertainties of $h$, $\tilde B\_\mathrm e$, $\pi$, $\tilde c$, and $\mu$ are not correlated, the total uncertainty of $r\_\mathrm e$ may be estimated using the [general formula](https://en.wikipedia.org/wiki/Propagation_of_uncertainty#Simplification):


$$u(r\_\mathrm e) = \sqrt{\left(\frac{\partial r\_\mathrm e}{\partial h}\right)^2 u^2(h)+\left(\frac{\partial r\_\mathrm e}{\partial \tilde B\_\mathrm e}\right)^2 u^2(\tilde B\_\mathrm e)+\left(\frac{\partial r\_\mathrm e}{\partial \pi}\right)^2 u^2(\pi)+\left(\frac{\partial r\_\mathrm e}{\partial \tilde c}\right)^2 u^2(\tilde c)+\left(\frac{\partial r\_\mathrm e}{\partial \mu}\right)^2 u^2(\mu)}$$


If only $\tilde B\_\mathrm e$ has a relevant uncertainty, the formula can be simplified to:


$$u(r\_\mathrm e) = \sqrt{\left(\frac{\partial r\_\mathrm e}{\partial \tilde B\_\mathrm e}\right)^2 u^2(\tilde B\_\mathrm e)}$$


where the partial derivative of $r\_\mathrm e$ with respect to $\tilde B\_\mathrm e$ is


$$\frac{\partial r\_\mathrm e}{\partial \tilde B\_\mathrm e}= - \frac{1}{8}\frac{{\sqrt 2 h}}{{\sqrt {\frac{h}{{\tilde B\_\mathrm e{\pi ^2}\tilde c\mu }}} {\tilde B\_{\mathrm e}^2}{\pi ^2}\tilde c\mu }}$$


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