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If y= log [x + sqrt(9 + x^(2))], "then"...

If ` y= log [x + sqrt(9 + x^(2))], "then" (dy)/(dx) ` is equal to

A

`(1)/(sqrt(9 + x^(2))`

B

`(9)/(sqrt(9 + x^(2)))`

C

`(1)/(sqrt( 9 - x^(2)))`

D

`- (1)/(sqrt(9 - x^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
A
Given , ` y = log (x + sqrt(9 + x^(2)))`
On differentiating both sides w.r.t.x, we get
`(dy)/(dx)=(1)/(x + sqrt(9 + x^(2))) xx(d)/(dx) (x + sqrt( 9 + x^(2)))`
` = (1)/(x + sqrt(9 + x^(2))) (1 + (1)/(2sqrt( 9 + x^(2)))xx(0+ 2x ))`
` = (1)/( x + sqrt(9 + x^(2))) xx((sqrt( 9 + x^(2)) + x)/(sqrt( 9 + x^(2)))) = (1)/(sqrt(9 + x^(2)))`
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