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If y""=""s e c(t a n^(-1)x) , then (dy)/...

If `y""=""s e c(t a n^(-1)x)` , then `(dy)/(dx)` at `x=1` is equal to (1) `1/2` (2) 1 (3) `sqrt(2)` (4) `1/(sqrt(2))`

A

`1//2`

B

1

C

`sqrt(2)`

D

`1sqrt(2)`

Text Solution

Verified by Experts

`y=sec(tan^(-1)x)`
`rArr" "(dy)/(dx)=sec (tan^(-1)x)cdottan (tan^(-1)x)cdot(1)/(1+x^(2))`
`rArr" "((dy)/(dx))_(x=1)=sec((pi)/(4))tan((pi)/(4))(1)/(1+1)=(1)/(sqrt(2))`
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