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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/sqrt2`

B

`1/2`

C

1

D

`sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
A
Given,` y = sec (tan^(1) x) `
Let `" " tan^(-1) x = theta`
` rArr" " x = tan theta`
` :." " y = tan theta = sqrt(1+x^(2)) `
On differentiating w.r.t. X, we get
`(dy)/(dx) = 1/(2sqrt(1+x^(2)) * 2x `
At ` x = 1, " " (dy)/(dx) = 1/(sqrt2) `
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