   Chapter 8.4, Problem 64E ### 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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# Finding Second Derivatives In Exercises 63–66, find the second derivative of the trigonometric function. y = sec   3 x

To determine

To calculate: The second derivative of the trigonometric function y=sec3x.

Explanation

Given Information:

The trigonometric function:

y=sec3x

Formula used:

Secant differentiation rule:

ddx[secu]=secutanududx

Tangent differentiation rule:

ddx[tanu]=sec2ududx

Product rule of differentiation:

ddx[a(x)b(x)]=a(x)b'(x)+b(x)a'(x)

General power rule of differentiation:

ddx[xn]=nxn1

Calculation:

Consider the trigonometric function:

y=sec3x

Apply the general power rule and secant rule of differentiation.

y'=ddx[sec3x]=3sec3xtan3x

Now, apply the product rule, general power rule, secant, and tangent rule of differentiation on the above function again

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