You can automatically take derivatives with the diff function. The one point to keep in mind is that the variable with respect to which you differentiate must be labeled as a Variable before defining the function to be differentiated. So, in this case, it would look something like:
u = variable(u)
F_inv = Fermi_inv(u)
dF_inv_du = diff(F_inv,u)
where dF_inv_du is \frac{d\mathcal{F}^{-1}(u)}{du}.