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Question
If y = sec (tan−1x) then `("d"y)/("d"x)` at x = 1 is ______.
Options
`1/2`
1
`1/sqrt(2)`
`sqrt(2)`
Solution
If y = sec (tan−1x) then `("d"y)/("d"x)` at x = 1 is `bb(1/sqrt(2))`.
Explanation:
[Hint : `"dy"/"dx" = sec(tan^-1x).tan(tan^-1x) xx (1)/(1 + x^2)`
∴ `(dy/dx)_("at" x = 1) = sec(tan^-1 1) xx 1 xx (1)/(1 + 1^2)`
= `sec pi/4 xx (1)/(2) = sqrt(2) xx (1)/(2) = (1)/sqrt(2)]`.
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