If f(x) = 2 sin^(-1) sqrt(1-x) + sin^(-1...

If `f(x) = 2 sin^(-1) sqrt(1-x) + sin^(-1)(2 sqrt(x (1-x)))` where `x in (0, 1/2)` , then `f'(x)` has the value equal to (i) `2/(xsqrt(1-x))` (ii) `0` (iii) `-2/(xsqrt(1-x))` (iv) `pi`

A

`(2)/(sqrt(x(-1)))`

B

Zero

C

`-(2)/(sqrt(x(-1)))`

D

`pi`

Verified by Experts

The correct Answer is:

B

f(x) simplifies to `pi`
`rArr f.(x)=0`
or directly differentiate f (x) to get zero

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