Answer
$\dfrac{1}{2 \sqrt{x(1+x)}} $
Work Step by Step
As we are given that $y=\sinh^{-1} \sqrt x$
Recall the formula: $\dfrac{d (\sinh^{-1} x)}{dx}=\dfrac{1}{\sqrt{1+x^2}}$
We need to use the chain rule to get the differentiation:
Thus, $\dfrac{dy}{dx}=\dfrac{1}{\sqrt{1+(\sqrt x)^2}} (\dfrac{1}{2 \sqrt x})=\dfrac{1}{2 \sqrt{x(1+x)}} $
