I need to calculate systematic error for \tau in capacitor's charging formula( V_{c}(t)=V_{s}(1-e^{\frac{t}{\tau}}) )

I converted it to : \tau=-{t \over ln(1-{V_c \over V_s})}
and continued by doing: ln(\tau)=ln(-t)-ln(ln(1-{V_c \over V_s}))
then tried to derivative: {d\tau \over \tau}={dt \over t}- ...
I can't go ahead any more!
How should i continue and get result for d\tau \over \tau?

Thanks