Question

Find the derivative of $f\left(x\right)=\frac{x+\cos x}{\tan x}w.r.t.x.$

Answer 1

$\frac{d}{dx}\left(\frac{u}{v}\right)=\frac{u^{1}v-u{v}^1}{v^2}$

$\Rightarrow \frac{d}{dx}\left(\frac{x+\cos x}{\tan x}\right)=\frac{(1-\sin x)\tan x-{\sec }^{2}x(x+\cos x)}{{\tan }^{2}x}$

$=\frac{\tan x-\sin x\tan x-x{\sec }^{2}x-\sec x}{{\tan }^{2}x}$.