   Chapter 8.4, Problem 38E ### 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 = sec 7 x 7 − sec 5 x 5

To determine

To calculate: The simplified derivative of the trigonometric function y=sec7x7sec5x5 using trigonometric identities.

Explanation

Given Information:

The trigonometric function:

y=sec7x7sec5x5

Formula used:

Secant differentiation rule:

ddx[secu]=secutanududx

General power rule of differentiation:

ddx[xn]=nxn1

The sum and difference formula of differentiation:

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

Pythagorean identity:

tan2θ=sec2θ1

Calculation:

Consider the trigonometric function:

y=sec7x7sec5x5

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

dydx=ddx[sec7x7]ddx[sec5x5]

Factor out the real numbers.

ddx[sec7x7]ddx[sec5x5]=17ddx[sec7x]15ddx[sec5x]

Now, apply the general power rule and secant rule of differentiation

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