Answer
$\dfrac{1}{2 \sqrt{x(1+x)}} $
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Work Step by Step
Given: $y=\sinh^{-1} \sqrt x$
Since, $\dfrac{d (\sinh^{-1} x)}{dx}=\dfrac{1}{\sqrt{1+x^2}}$
Thus, $\dfrac{dy}{dx}=\dfrac{1}{\sqrt{1+(\sqrt x)^2}} (\dfrac{1}{2 \sqrt x})$
or, $=\dfrac{1}{2 \sqrt{x(1+x)}} $
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