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If y=sqrt(sinsqrt(x))then (dy)/(dx) is :...

If `y=sqrt(sinsqrt(x))`then `(dy)/(dx)` is `:`

A

`(1)/(4sqrt(x)).(cossqrt(x))/(sinsqrt(x))`

B

`(1)/(4sqrt(x)).sqrt(tansqrt(x))sqrt(cossqrt(x))`

C

`(1)/(4sqrt(x))sqrt((cossqrtx)/(sinsqrt(x)))`

D

`(1)/(4sqrt(x)).sqrt(cotsqrtx).sqrt(cossqrt(x))`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)/(dx)[(sinsqrt(x))^(1//2)]=(1)/(2)(sinsqrt(x))^(-1//2).[cossqrt(x)].(1)/(2)`
`(x)^(-1//2)(` By power chain rule `)`
`=(1)/(4sqrt(x)).(cossqrt(x))/(sqrt(sinsqrt(x)))=(1)/(4sqrt(x)).sqrt(cotsqrt(x)).sqrt(cossqrt(x))`
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