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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

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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