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If y=sec^(-1)((sqrt(x-1))/(x+sqrt(x)))+...

If `y=sec^(-1)((sqrt(x-1))/(x+sqrt(x)))+sin^(-1)((x+sqrt(x))/(sqrt(x-1)))`, then `(dy)/(dx)=` ……………

A

x

B

`(1)/(x)`

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
Given , `y=sec^(-1)((sqrt(x)-1)/(x+sqrt(x)))+sin^(-1)((x+sqrt(x))/(sqrt(x)-1))`
`y=cos^(-1)((x+sqrt(x))/(sqrt(x-1)))+sin^(-1)((x+sqrt(x))/(sqrt(x-1)))`
`y=(pi)/(2)[becausesin^(-1)x+cos^(-1)x=(pi)/(2)]`
`therefore(dy)/(dx)=0`
Hence the correct answer from the given alternative is .
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