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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![**Problem:**
Find \(\frac{d}{dx} (5 \ln(x))\).
**Solution:**
To find the derivative of the function \(5 \ln(x)\), we use the derivative rule for a constant multiplied by a function. The derivative of \(c \cdot f(x)\), where \(c\) is a constant, is \(c \cdot f'(x)\).
Given:
- \(f(x) = \ln(x)\)
- \(f'(x) = \frac{1}{x}\) (the derivative of \(\ln(x)\))
Now, apply the constant multiple rule:
\[
\frac{d}{dx} (5 \ln(x)) = 5 \cdot \frac{d}{dx} (\ln(x)) = 5 \cdot \frac{1}{x} = \frac{5}{x}
\]
So, the derivative of \(5 \ln(x)\) is \(\frac{5}{x}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa35d32dc-632b-40fd-aa41-e2c0040899b1%2F117c73ac-8b5c-4428-aaa3-74b3c66c22e1%2Fkg2nbqq_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem:**
Find \(\frac{d}{dx} (5 \ln(x))\).
**Solution:**
To find the derivative of the function \(5 \ln(x)\), we use the derivative rule for a constant multiplied by a function. The derivative of \(c \cdot f(x)\), where \(c\) is a constant, is \(c \cdot f'(x)\).
Given:
- \(f(x) = \ln(x)\)
- \(f'(x) = \frac{1}{x}\) (the derivative of \(\ln(x)\))
Now, apply the constant multiple rule:
\[
\frac{d}{dx} (5 \ln(x)) = 5 \cdot \frac{d}{dx} (\ln(x)) = 5 \cdot \frac{1}{x} = \frac{5}{x}
\]
So, the derivative of \(5 \ln(x)\) is \(\frac{5}{x}\).
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