Explanation Concept Used: The quotient rule of derivatives: d d x [ f ( x ) g ( x ) ] = g ( x ) ⋅ d d x f ( x ) − f ( x ) ⋅ d d x g ( x ) ( g ( x ) ) 2 Power rule of derivatives: d d x ( x n ) = n x n − 1 d d x ( cos x ) = − sin x Trigonometric ratios: sec x = 1 cos x , tan x = sin x cos x Calculation: In order to prove the given derivative formula, first write the function as a trigonometric ratio in terms of cosine. So, it gives d d x ( sec x ) = d d x ( 1 cos x ) Observe that the given function is a quotient of two functions 1 and ( cos x )

15th Edition

ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Chapter 3.4, Problem 46E

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Prove that, ddx(secx)=secxtanx .

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Chapter 3.4, Problem 45E

Chapter 3.4, Problem 47E

Chapter 3 Solutions

Biocalculus: Calculus For Life Sciences

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Prove that, d d x ( sec x ) = sec x tan x .

Solution Summary: The author explains that the given function is a quotient of two functions 1andleft.

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Prove that, ddx(secx)=secxtanx .

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Chapter 3 Solutions