Question

Find the derivative of $\frac{x+\cos x}{\tan x}$

Answer 1

Let $y=\frac{x+\cos x}{\tan x}$ ………….$\left(1\right)$

differentiating equation $\left(1\right)$ wrt x we get

$\frac{dy}{dx}=\frac{d}{dx}\left(\frac{x+\cos x}{\tan x}\right)$

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

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