Answer
$$ y'= \frac{x^{-2}}{|x^{-1}|\sqrt{(x^{-1})^2-1}}=\dfrac{1}{\sqrt{1-x^2}} .$$
Work Step by Step
Since $ y=\csc^{-1}(x^{-1})$, then the derivative $ y'$ is given by
$$ y'= -\frac{1}{|x^{-1}|\sqrt{(x^{-1})^2-1}} (x^{-1})'= \frac{x^{-2}}{|x^{-1}|\sqrt{(x^{-1})^2-1}} .$$
This can be simplified to:
$$y'=\dfrac{1}{\sqrt{1-x^2}}$$
