Answer
$\frac{1}{\sqrt {x^3}}csc^2(\frac{1}{\sqrt x})dx$
Work Step by Step
Given $y=2cot(\frac{1}{\sqrt x})$, we have $dy=-2csc^2(\frac{1}{\sqrt x})(-\frac{1}{2\sqrt {x^3}})dx=csc^2(\frac{1}{\sqrt x})(\frac{1}{\sqrt {x^3}})dx=\frac{1}{\sqrt {x^3}}csc^2(\frac{1}{\sqrt x})dx$
