   Chapter 8.4, Problem 35E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Differentiating Trigonometric Functions In Exercises 29-40, find the derivative of the function and simplify your answer by using the trigonometric identities listed in Section 8.2. y = tan   x − x

To determine

To calculate: The simplified derivative of the trigonometric function y=tanxx using trigonometric identities.

Explanation

Given Information:

The provided trigonometric function is y=tanxx.

Formula used:

Tangent differentiation rule:

ddx[tanu]=sec2ududx

General power rule of differentiation:

ddx[xn]=nxn1

The sum and difference formula of differentiation:

ddx[f(x)+g(x)]=f(x)+g(x)

Trigonometric identity,

tan2θ=sec2θ1

Calculation:

Consider the provided trigonometric function is,

y=tanxx

Apply the sum and difference formula of differentiation on the above function

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