Question

Find the derivative of $\frac{x+\cos x}{\tan x}$ with respect to $x$.

Answer 1

Given function is $\frac{x+\cos x}{\tan x}$

This form is in $\frac{u}{v}$ form,

$\therefore$ differentiating with respect to $x$ gives,

$\frac{\tan x(1-\sin x)-(x+\cos x){\sec }^{2}x}{{\tan }^{2}x}=\frac{\tan x-\tan x.\sin x-x{\sec }^{2}x-\sec x}{{\tan }^{2}x}$