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

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

A

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

B

Zero

C

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

D

`pi`

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)` simplifies to `pi`
`rArr" "f'(x)=0`
or `" "`directly differentiale `f(x)` to get zone
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