Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.4 Derivatives of Trigonometric Functions - 2.4 Exercises - Page 150: 9


$y'=\dfrac{2-\tan x+x\sec^2 x}{(2 -\tan x)^2}$

Work Step by Step

Given: $y=\dfrac{x}{2 -\tan x}$ On differentiating w.r.t. $x$ , we get Apply product rule. $y'=\dfrac{d}{dx}(\dfrac{x}{2 -\tan x})\\=\dfrac{(2-\tan x)(1)-x(-\sec^2 x)}{(2 -\tan x)^2}\\=\dfrac{2-\tan x+x\sec^2 x}{(2 -\tan x)^2}$
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