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

If `y=e^(sqrt(x))+e^(-sqrt(x))` , then `(dy)/(dx)i se q u a lto` `(e^(sqrt(x)))/(2sqrt(x))` (b) `(e^(sqrt(x))-e^(-sqrt(x)))/(2x)` `1/(2sqrt(x))sqrt(y^2-4)` (d) `1/(2sqrt(x))sqrt(y^2+4)`

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

Verified by Experts

`(dy)/(dx)=(e^(sqrt(x)))/(2sqrt(x))-(e^(-sqrt(x)))/(2sqrt(x))=(e^(sqrt(x)-)e^(-sqrt(x)))/(2sqrt(x))`
`=(sqrt((e^(sqrt(x))+e^(-sqrt(x)))^(2))-4)/(2sqrt(x))`
`=(sqrt(y^(2)-4))/(2sqrt(x))`
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If y=e^(sqrt(x))+e^(-sqrt(x)) , then (dy)/(dx) is equal to (a) (e^(sqrt(x)))/(2sqrt(x)) (b) (e^(sqrt(x))-e^(-sqrt(x)))/(2x) 1/(2sqrt(x))sqrt(y^2-4) (d) 1/(2sqrt(x))sqrt(y^2+4)

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Knowledge Check

  • int e^(sqrt(x)) dx is

    A
    `2sqrt(x)(1-e^(sqrt(x)))+c`
    B
    `2sqrt(x)(e^(sqrt(x))-1)+c`
    C
    `2e^(sqrtx)(1-sqrt(x))+c`
    D
    `2e^(sqrt(x))(sqrt(x)-1)+c`

  • int e^(sqrt(x)) dx is

    A
    `2 sqrt( x) ( 1 - e ^(sqrt(x)))`+ c
    B
    `2 sqrt( x) ( e ^(sqrt(x))-1)`+ c
    C
    ` 2e^(sqrt(x)) (1 - sqrt(x)) + c `
    D
    ` 2e^(sqrt(x)) ( sqrt(x)-1) + c `

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