By chain rule $\frac{1}{\sqrt{x}} (\csc^2 )' (\sqrt{x})$.
So now compute the derivative of $\csc^2$ by writing it as $\frac{\cos^2 }{\sin^2 }$ and using the quotient rule.
All you do now if substitute $\sqrt{x}$ into that result. And that gives you the value of $(\csc^2 x)'(\sqrt{x})$.