Find the derivative of the following function: (sec x - 1)/(sec x + 1)

Solution:

The given function is f(x) = (sec x - 1)/(sec x + 1).

Its derivative using the quotient rule is,

d/dx (f(x)) = [ (sec x + 1) d/dx (sec x - 1) - (sec x - 1) d/dx (sec x + 1) ] / (sec x + 1)²

= [ (sec x + 1) (sec x tan x) - (sec x - 1) (sec x tan x) ] / (sec x + 1)² (using derivative formulas)

= [ sec²x tan x + sec x tan x - sec²x tan x + sec x tan x ] / (sec x + 1)²

= [ 2 sec x tan x ] / (sec x + 1)²

NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 18

Find the derivative of the following function: (sec x - 1)/(sec x + 1)

Summary:

The derivative of the given function (sec x - 1)/(sec x + 1) is [ 2 sec x tan x ] / (sec x + 1)²