Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![### Calculus Exercise:
**Problem Statement:**
Given the function \( f(x) = \sin^5 x \), find the derivative \( f'(x) \).
**Solution:**
Using the chain rule for derivatives, the derivative of \( f(x) = \sin^5 x \) is:
\[ f'(x) = 5 \sin^4(x) \cos(x) \]
**Next Step:**
To find \( f'(2) \), further calculation is required using the derivative function \( f'(x) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e51674d-3d29-4cb4-94ad-529601d10286%2F7f5a1129-8f70-43cc-89c6-5b68e8c5bd01%2Fnwvzyhi_processed.png&w=3840&q=75)
Transcribed Image Text:### Calculus Exercise:
**Problem Statement:**
Given the function \( f(x) = \sin^5 x \), find the derivative \( f'(x) \).
**Solution:**
Using the chain rule for derivatives, the derivative of \( f(x) = \sin^5 x \) is:
\[ f'(x) = 5 \sin^4(x) \cos(x) \]
**Next Step:**
To find \( f'(2) \), further calculation is required using the derivative function \( f'(x) \).
![If \( f(x) = 2 \sec(3x) \), find \( f'(x) \).
- **Solution:** \( 6 \sec(3x) \tan(3x) \)
Find \( f'(5) \).
- **Solution:** [Blank for user input]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e51674d-3d29-4cb4-94ad-529601d10286%2F7f5a1129-8f70-43cc-89c6-5b68e8c5bd01%2Fdj8e7dp_processed.png&w=3840&q=75)
Transcribed Image Text:If \( f(x) = 2 \sec(3x) \), find \( f'(x) \).
- **Solution:** \( 6 \sec(3x) \tan(3x) \)
Find \( f'(5) \).
- **Solution:** [Blank for user input]
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