Mathematics · JEE | LIMITS AND DERIVATIVES

Find the derivative of \( f(x) = \frac{x + \cos x}{\tan x} \).

1. A
   \( \frac{(1 - \sin x)\tan x - (x + \cos x)\sec^2 x}{\tan^2 x} \)
2. B
   \( \frac{(1 + \sin x)\tan x + (x + \cos x)\sec^2 x}{\tan^2 x} \)
3. C
   \( \frac{\sin x \tan x - (x + \cos x)\sec^2 x}{\tan^2 x} \)
4. D
   \( \frac{(1 - \sin x)\tan x + (x + \cos x)\sec^2 x}{\tan^2 x} \)