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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![The image contains a mathematical expression related to differentiation rules, specifically the power rule for derivatives and its application.
1. **Power Rule for Derivatives**:
- The formula shown is: \( \frac{d}{dx}(x^n) = nx^{n-1} \)
- This rule states that the derivative of \( x^n \) with respect to \( x \) is \( n \) times \( x \) raised to the power of \( n-1 \).
2. **Application of the Power Rule**:
- The text mentions the application of the power rule to a specific function.
- The expression is:
\[
9e^x + 2 \frac{d}{dx}\left(x^{-1/3}\right) = 9e^x - \boxed{\phantom{}}\)
\]
- The derivative of \( x^{-1/3} \) needs to be calculated using the power rule, and the result will complete the equation within the box.
- In this context, \( x^{-1/3} \) is differentiated, and the result should replace the box to find the complete expression.
No graphs or diagrams are present in the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0fac6bec-f0b2-4056-963f-cf73547656d5%2Ff0254832-28e3-408b-9ece-a80d39705922%2Ft03hlis_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a mathematical expression related to differentiation rules, specifically the power rule for derivatives and its application.
1. **Power Rule for Derivatives**:
- The formula shown is: \( \frac{d}{dx}(x^n) = nx^{n-1} \)
- This rule states that the derivative of \( x^n \) with respect to \( x \) is \( n \) times \( x \) raised to the power of \( n-1 \).
2. **Application of the Power Rule**:
- The text mentions the application of the power rule to a specific function.
- The expression is:
\[
9e^x + 2 \frac{d}{dx}\left(x^{-1/3}\right) = 9e^x - \boxed{\phantom{}}\)
\]
- The derivative of \( x^{-1/3} \) needs to be calculated using the power rule, and the result will complete the equation within the box.
- In this context, \( x^{-1/3} \) is differentiated, and the result should replace the box to find the complete expression.
No graphs or diagrams are present in the image.
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