I need to calculate systematic error for $\tau$ in capacitor's charging formula($V_c(t)=V_s\left(1-e^{-t\over\tau}\right)$ )
I converted it to : $\tau=-{t \over \ln(1-{V_c \over V_s})}$
and continued by doing: $\ln(\tau)=\ln(-t)-\ln\left(\ln\left(1-{V_c \over V_s}\right)\right)$
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 $d\tau \over \tau$?