Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question

Find derivative, and explain step by step.

21. y = csc ³ (cos 8x)
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Transcribed Image Text:21. y = csc ³ (cos 8x)
Expert Solution
Check Mark
Step 1: Introduction

Given, 

         y equals text csc end text cubed space open parentheses cos open parentheses 8 x close parentheses close parentheses

The aim is to find the derivative of the above function.

Concept used :

The chain rule states that the derivative of f left parenthesis g left parenthesis x right parenthesis right parenthesis is fraction numerator d over denominator d x end fraction open square brackets f open curly brackets g left parenthesis x right parenthesis close curly brackets close square brackets times fraction numerator d over denominator d x end fraction left parenthesis g left parenthesis x right parenthesis right parenthesis.

The formula used here:

1. Derivative of text csc end text left parenthesis x right parenthesis with respect to x,

fraction numerator d over denominator d x end fraction left parenthesis text csc end text space x right parenthesis equals negative text cot end text space x times text csc end text space x

2. Derivative of cos left parenthesis x right parenthesis with respect to x,

fraction numerator d over denominator d x end fraction left parenthesis cos space x right parenthesis equals negative sin left parenthesis x right parenthesis

3. Derivative of x to the power of n with respect to x

fraction numerator d over denominator d x end fraction left parenthesis x to the power of n right parenthesis equals n x to the power of n minus 1 end exponent


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