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
![**Problem Statement:**
Find \( y' \).
\[ y = 9x - \ln(2x) \]
\[ y' = \]
**Solution Explanation:**
To find the derivative of the function \( y = 9x - \ln(2x) \), we will differentiate each term separately.
1. **Differentiating \( 9x \):**
The derivative of \( 9x \) with respect to \( x \) is \( 9 \).
2. **Differentiating \( \ln(2x) \):**
Using the chain rule, the derivative of \( \ln(2x) \) is \(\frac{1}{2x} \times 2 = \frac{1}{x}\).
Combining these results, the derivative \( y' \) is:
\[ y' = 9 - \frac{1}{x} \]
This derivative represents the rate of change of the function \( y \) with respect to \( x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7aab756-0f3b-421c-a400-c3f015f6942d%2Fec2e1bb1-8bc5-4b48-a193-5f81b2915ad4%2F5tiake_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find \( y' \).
\[ y = 9x - \ln(2x) \]
\[ y' = \]
**Solution Explanation:**
To find the derivative of the function \( y = 9x - \ln(2x) \), we will differentiate each term separately.
1. **Differentiating \( 9x \):**
The derivative of \( 9x \) with respect to \( x \) is \( 9 \).
2. **Differentiating \( \ln(2x) \):**
Using the chain rule, the derivative of \( \ln(2x) \) is \(\frac{1}{2x} \times 2 = \frac{1}{x}\).
Combining these results, the derivative \( y' \) is:
\[ y' = 9 - \frac{1}{x} \]
This derivative represents the rate of change of the function \( y \) with respect to \( x \).
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