A) 0
B) \[\frac{1}{\sqrt{x}+1}\]
C) 1
D) None of these
Correct Answer: A
Solution :
\[y={{\sec }^{-1}}\left( \frac{\sqrt{x}+1}{\sqrt{x}-1} \right)+{{\sin }^{-1}}\left( \frac{\sqrt{x}-1}{\sqrt{x}+1} \right)\] \[={{\cos }^{-1}}\left( \frac{\sqrt{x}-1}{\sqrt{x}+1} \right)+{{\sin }^{-1}}\left( \frac{\sqrt{x}-1}{\sqrt{x}+1} \right)=\frac{\pi }{2}\] Þ \[\frac{dy}{dx}=0\] , \[\left\{ \because {{\sin }^{-1}}x+{{\cos }^{-1}}x=\frac{\pi }{2} \right\}\].
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