## University Calculus: Early Transcendentals (3rd Edition)

$\dfrac{1}{2 \sqrt{x(1+x)}}$
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, $\dfrac{dy}{dx}=\dfrac{1}{\sqrt{1+(\sqrt x)^2}} (\dfrac{1}{2 \sqrt x})=\dfrac{1}{2 \sqrt{x(1+x)}}$