Differentiate the following functions with respect to x :
sec x−1sec x+1
Let y = sec x−1sec x+1
Differentiating y w.r.t. x, we get
dydx=(sec x+1)ddx(sec x−1)−(sec x−1)ddx(sec x+1)(sec x+1)2 (By quotient formula)
=(sec x+1)(sec x tan x−0)−(sec x−1)(sec x tan x+0)(sec x+1)2
=(sec x+1)(sec x tan x)−(sec x−1)(sec x tan x)(sec x+1)2
=sec x tan x[sec x+1−sec x+1](sec x+1)2=2 sec x tan x(sec x+1)2