Find the derivative of x + x x . - Vidyadip

Question

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

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Answer

Let $y = \frac { x + \cos x } { \tan x }$
On differentiating both sides w.r.t. x, we get
$\frac { d y } { d x } = \frac { \frac { d } { d x } \tan x ( x + \cos x ) - ( x + \cos x ) \frac { d } { d x } ( \tan x ) } { ( \tan x ) ^ { 2 } }$ [using quotient rule of derivate]
$= \frac { \tan x ( 1 - \sin x ) - ( x + \cos x ) \sec ^ { 2 } x } { ( \tan x ) ^ { 2 } }$

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