Explanation Given: The function, f ( x ) = 1 − sec x tan x . 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 ( sec x ) = sec x tan x d d x ( tan x ) = sec 2 x Calculation: In order to find the derivative of the given function, use the quotient rule of derivatives. Observe that the given function is a quotient of two functions 1 − sec x and ( tan x ) . So, using the quotient rule and power rule of derivatives, it gives y ' = d d x ( 1 − sec x tan x ) = ( tan x ) ⋅ d d x ( 1 − sec x ) − ( 1 − sec x

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ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Chapter 3.4, Problem 26E

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The derivative of the function, f(x)=1−secxtanx .

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Chapter 3.4, Problem 25E

Chapter 3.4, Problem 27E

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Chapter 3 Solutions

Biocalculus: Calculus For Life Sciences

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The derivative of the function, f ( x ) = 1 − sec x tan x .

Solution Summary: The author explains how to find the derivative of the given function using the quotient rule of derivatives.

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The derivative of the function, f(x)=1−secxtanx .

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