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d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^...

`d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]=` `1/(sqrt(1-x^2))-1/(2sqrt(x-x^2))` `(-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2))` `1/(sqrt(1-x^2))+1/(2sqrt(x-x^2))` `1/(sqrt(1-x^2))` `0` b. `1//4` c. `-1//4` d. none of these

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
`y=cos^(-1)[xsqrtx-sqrt(1-(sqrtx)^(2))sqrt(1-x^(2))]`
`=cos^(-1)x+cos^(-1)sqrtx`
`therefore" "(dy)/(dx)=(-1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))`
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