derivative problem in calculating Systematic Error for capacitor charge time constat

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

I converted it to : $\displaystyle \tau=-{t \over ln(1-{V_c \over V_s})}$

and continued by doing: $\displaystyle ln(\tau)=ln(-t)-ln(ln(1-{V_c \over V_s}))$

then tried to derivative: $\displaystyle {d\tau \over \tau}={dt \over t}- ...$

I can't go ahead any more!

How should i continue and get result for $\displaystyle d\tau \over \tau$?

Thanks