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If y=e^(sqrt(x))+e^(-sqrt(x)), then (d...

If `y=e^(sqrt(x))+e^(-sqrt(x))`, then `(dy)/(dx)` is equal to -

A

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

B

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

C

`(1)/(2sqrt(x))sqrt(y^(2)-4)`

D

`(1)/(2sqrt(x))sqrt(y^(2)+4)`

Text Solution

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The correct Answer is:
A, C
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Knowledge Check

  • Let y=sqrt(x+sqrt(x+sqrt(x+...oo))) , then (dy)/(dx) is equals to -

    A
    `(1)/(2y-1)`
    B
    `(x)/(x+2y)`
    C
    `(1)/(sqrt(1+4x))`
    D
    `(y)/(x+2y)`

  • If y=sqrt(sin sqrt(x)) , then the value of (dy)/(dx) is -

    A
    `(1)/(2sqrt(sin sqrt(x)))`
    B
    `(sqrt(cos sqrt(x)))/(2x)`
    C
    `(1)/(2sqrt(cos sqrt(x)))`
    D
    `(cos sqrt(x))/(4sqrt(x)sqrt(sin sqrt(x)))`

  • If y=sqrt(x+sqrt(y+sqrt(x+sqrty+...oo))) then (dy)/(dx) equal to

    A
    `(y^2-x)/(2y^3-2xy-1)`
    B
    `(y^2+x)/(2y^3+2xy+1)`
    C
    `(x^2+x)/(2y^3-2xy-1)`
    D
    none of these

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