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प्रश्न
If y = sec (tan−1x), then `dy/dx` at x = 1 is ______.
विकल्प
`1/2`
1
`1/sqrt(2)`
`sqrt(2)`
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उत्तर
If y = sec (tan−1x), then `dy/dx` at x = 1 is `underlinebb(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 π/4 xx (1)/(2) = sqrt(2) xx (1)/(2) = (1)/sqrt(2).]`
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