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Question

Differentiate the following functions with respect to x :

sec x1sec x+1

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Solution

Let y = sec x1sec x+1

Differentiating y w.r.t. x, we get

dydx=(sec x+1)ddx(sec x1)(sec x1)ddx(sec x+1)(sec x+1)2 (By quotient formula)

=(sec x+1)(sec x tan x0)(sec x1)(sec x tan x+0)(sec x+1)2

=(sec x+1)(sec x tan x)(sec x1)(sec x tan x)(sec x+1)2

=sec x tan x[sec x+1sec x+1](sec x+1)2=2 sec x tan x(sec x+1)2


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