Answer
$\dfrac{1}{2 \sqrt t}-\coth^{-1} \sqrt t$
Work Step by Step
Given: $y=(1-t) \coth^{-1} \sqrt t$
Since, $\dfrac{d (\coth^{-1} x)}{dx}=\dfrac{1}{1-x^2}$
Apply product rule to get the differentiation.
Thus, $\dfrac{dy}{dt}=(1-t) \dfrac{1}{1-(\sqrt t)^2} \dfrac{1}{2 \sqrt t}-\coth^{-1} \sqrt t$
or, $=\dfrac{1}{2 \sqrt t}-\coth^{-1} \sqrt t$
