Answer
$\dfrac{1}{2 \sqrt t}-\coth^{-1} \sqrt t$
Work Step by Step
We are given: $y=(1-t) \coth^{-1} \sqrt t$
Recall the formula: $\dfrac{d (\coth^{-1} x)}{dx}=\dfrac{1}{1-x^2}$
We need to use the product rule to get the differentiation:
$\dfrac{dy}{dt}=(1-t) \dfrac{1}{1-(\sqrt t)^2} \dfrac{1}{2 \sqrt t}-\coth^{-1} \sqrt t=\dfrac{1}{2 \sqrt t}-\coth^{-1} \sqrt t$
