Question

Differentiate with respect to x secx-1/secx+1

Answer 1

 y = [sec x-1] / [sec x+1] 
y = [sec x + 1 -1 -1] / [sec x+1] 
y = 1 - 2 / [sec x+1] 
y = 1 - 2 cos x / [cos x + 1] 
dy/dx = - 2 [- sin x (1+cos x) - (- sin x) cos x] / (1+cos x)^2 
dy/dx = - 2 [- sin x - sin x cos x + sin x cos x] / (1+cos x)^2 
dy/dx = - 2 [- sin x ] / (1+cos x)^2 
dy/dx = 2 sin x / (1+cos x)^2 
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how it is same as that of Hemant below 
2 sin x / (1+cos x)^2 = 2*2 sin x/2 cos x/2 / 4 cos^4 x/2 
2 sin x / (1+cos x)^2 = sin x/2 /cos^3 x/2 
2 sin x / (1+cos x)^2 = tan x/2 * sec^2 x/2 = Hemant's






bro,u seriously in primary school

Answer 2

secx-1/secx+1

Using quotient rule

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

=secx+1(secxtanx-0)- secx-1(secxtanx+0) / (secx+1)^2

=sec^2xtanx+ secxtanx-secx^2tanx+secxtanx

= 2secxtanx/ (secx+1)^2