Question

Choose the correct option from the given alternatives :

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

Options

• `(1)/(2)`

• 1

• `(1)/sqrt(2)`

• `sqrt(2)`

Answer 1

`(1)/sqrt(2)`

[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)].`