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If y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(d...

If `y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx)` is `(n y)/(sqrt(x^2+a^2))` (b) `-(n y)/(sqrt(x^2+a^2))` `(n x)/(sqrt(x^2+a^2))` (d) `-(n x)/(sqrt(x^2+a^2))`

A

`(ny)/(sqrt(x^(2)+a^(2))`

B

`-(ny)/(sqrt(x^(2)+a^(2))`

C

`(nx)/(sqrt(x^(2)+a^(2))`

D

`-(nx)/(sqrt(x^(2)+a^(2))`

Text Solution

Verified by Experts

`(dy)/(dx)=(d)/(dx)[(x+sqrt(x^(2)+a^(2)))^(n)]`
`=n(x+sqrt(x^(2)+a^(2)))^(n-1).(d)/(dx)(x+sqrt(x^(2)+a^(2)))`
`n=(x+sqrt(x^(2)+a^(2)))^(n-1)((sqrt(x^(2)+a^(2))+x)/(sqrt(x^(2))+a^(2)))`
`=(n(x+sqrt(x^(2)+a^(2)))^(n))/(sqrt(x^(2))+a^(2))`
`=(ny)/(sqrt(x^(2))+a^(2))`
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