   Chapter 8.4, Problem 14E ### 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 1-28, find the derivative of the trigonometric function. See Examples 1, 2, 3, y  =  sin  6 x 3

To determine

To calculate: The derivative of the trigonometric function y=sin6x3.

Explanation

Given Information:

The provided trigonometric function is y=sin6x3.

Formula used:

Sine differentiation rule:

ddx[sinu]=cosududx

General power rule of differentiation:

ddx[xn]=nxn1

Calculation:

Consider the provided trigonometric function is,

y=sin6x3

Let u=sin6x then the function will become:

y=u3=u1/3

Differentiate the above function using general power rule.

dydx=ddx[u1/3]=13u2/3dudx

Now, substitute back u=sin6x in the above function and differentiate the function using Sine differentiate rule and general power rule

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