Answer
$\frac{ds}{dt}={\frac{{-1}}{2\sqrt{t}}{(\sqrt{t}-1)}^{-2}}$
Work Step by Step
Given $s=\frac{1}{(\sqrt{t}-1)}$
$s={(\sqrt{t}-1)}^{-1}$
on differentiating both sides:
$\frac{ds}{dt}=\frac{d({(\sqrt{t}-1)}^{-1})}{dt}$
$\frac{ds}{dt}={-1}{(\sqrt{t}-1)}^{-2}{\frac{d({(\sqrt{t}-1)})}{dt}}$
$\frac{ds}{dt}={-1}{(\sqrt{t}-1)}^{-2}{\frac{{1}}{2\sqrt{t}}}$
$\frac{ds}{dt}={\frac{{-1}}{2\sqrt{t}}{(\sqrt{t}-1)}^{-2}}$
