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Given y = sqrta^sqrt(x), "then" (dy)/(dx...

Given `y = sqrta^sqrt(x), "then" (dy)/(dx)` is equal to

A

`(y)/(2) ( sqrta^sqrt(x)log a)/(4y sqrt(x))`

B

`(y)/(2)`

C

` ( sqrta^sqrt(x)log a)/(4y sqrt(x))`

D

`s^(sqrt(x)) log a `

Text Solution

Verified by Experts

The correct Answer is:
C
Given ` y sqrt(a^(sqrt(x)))`
` (dy)/(dx) = (1)/(2sqrt(a^(sqrt(x))) )xx(d)/(dx) (a^(sqrt(x)))`
` (1)/(2sqrt(a^(sqrt(x))) )xxa^(sqrt(x))log a (d)/(dx) (sqrt(x))`
`(a^(sqrt(x))loga)/(2sqrt(a^sqrt(x)))xx(1)/(2sqrt(x)) = (a^(sqrt(x))log a )/(4y sqrt(x))`
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Knowledge Check

  • If y = x^sqrt(x) , "then "(dy)/(dx) is equal to

    A
    `(y)/(sqrt(x)) (2 + log x)`
    B
    `(y)/(2 sqrt(x)) (2 + log x)`
    C
    `(y)/(sqrt(x)) (2 - log x)`
    D
    `(y)/(2sqrt(x)) (2 - log x)`

  • If y = sin^(-1) sqrt(1-x), "then " (dy)/(dx) is equal to

    A
    `(1)/(sqrt(1 -x))`
    B
    `(-1)/(2sqrt(1 -x))`
    C
    `(1)/(sqrt(x))`
    D
    `(-1)/(2sqrt(x)sqrt(1 -x))`

  • If y = sqrt(sin + y ) "then" (dy)/(dx) is equal to

    A
    `(cos x )/(2y -1)`
    B
    `(cos x )/(1 - 2y)`
    C
    `(sin x )/(1 - 2y)`
    D
    `(sin x)/(2y - 1)`

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