1.

If `y=sec^(-1)((sqrt(x-1))/(x+sqrt(x)))+sin^(-1)((x+sqrt(x))/(sqrt(x-1)))`, then `(dy)/(dx)=` ……………A. xB. `(1)/(x)`C. 1D. 0

Answer» Correct Answer - 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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