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Find $\cfrac{dy}{dx}$ if $y=\sec^{-1} \sqrt{x}$.

A

$\cfrac{1}{2x\sqrt{x-1}}$

B

$\cfrac{1}{\sqrt{x^2-x}}$

C

$\cfrac{1}{2x\sqrt{x^2-1}}$

D

$\cfrac{1}{2\sqrt{x} (1+x)}$

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