Question

If f(x) = log (sec x + tan x), then `"f'"(π/4)` = ____________.

Options

• `1/sqrt2`

• `sqrt2`

• 1

• `2/sqrt3`

Answer 1

If f(x) = log (sec x + tan x), then `"f'"(π/4)` = `underline(sqrt2)`.

Explanation:

We have, f(x) = log (sec x + tan x)

f'(x) = `1/(sec "x" + tan "x") (sec "x" tan "x" + sec^2 "x")`

f'(x) = `(sec "x" (sec "x" + tan "x"))/(sec "x" + tan "x")`

f'(x) = sec x

 `"f'"(π/4) = sec (π/4) = sqrt2`