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: 18


$\dfrac{d}{dx}( \sec x)= \sec x \tan x$

Work Step by Step

Need to prove $\dfrac{d}{dx}( \sec x)= \sec x \tan x$ Consider left hand side. $\dfrac{d}{dx}( \sec x)=\dfrac{d}{dx}( \dfrac{1}{\cos x})\\=\dfrac{ \sin x}{ \cos^2 x}\\=(\dfrac{1}{\cos x})(\dfrac{\sin x}{\cos x})\\= \sec x \tan x$
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