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"If "y=sec (tan^(-1)x)," then "(dy)/(dx)...

`"If "y=sec (tan^(-1)x)," then "(dy)/(dx)" at "x=1` is equal to

A

`(1)/(sqrt(2))`

B

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

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`y=sec(tan^(-1)x)`
`implies" "y=sec(sec^(-1)sqrt(1+x^(2))`
`implies" "y=sqrt(1+x^(2))implies(dy)/(dx)=(x)/(sqrt(1+x^(2)))implies((dy)/(dx))_(x=1)=(1)/(sqrt(2))`
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