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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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  • If y =sqrt (tan sqrt x ), then (dy)/(dx) =

    A
    `(sec^(2)sqrtx)/( 4sqrt(xtan sqrt x)) `
    B
    ` (sec ^(2)sqrt x)/( 2sqrt(xtan sqrtx))`
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    A
    `(cos x)/(2y-1)`
    B
    `(cos x)/(1-2y)`
    C
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    D
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  • If y= sin sqrt ( sin sqrt x) ,then (dy)/( dx) =

    A
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