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If y= log (sqrt(x - 1)) - sqrt(x + 1)) ...

If ` y= log (sqrt(x - 1)) - sqrt(x + 1)) , "then " (dy)/(dx) ` is equal to

A

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

B

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

C

`(1)/(2sqrt(x - 1)) -(1)/(2sqrt(x + 1))`

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Given , ` y = log (sqrt(x -1)) - sqrt(x +1))`
On differentiating both sides w.r.t.x., we get
`(dy)/(dx) = (1)/((sqrt(x -1) - sqrt(x +1)))xx((1)/(2sqrt(x -1)) - (1)/(2sqrt( x +1)))`
` = (sqrt(x +1)-sqrt(x-1))/(sqrt(x -1) - sqrt(x +1)) xx(1)/(2sqrt( x^(2) -1))=-(1)/(2sqrt( x^(2) -1))`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 1 DERIVATIVE OF COMPOSITE FUNCTION (BY CHAIN RULE )
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