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 the derivative of the function.
Given:
\[ g(s) = 9s^2 - \frac{8}{s} + \frac{8}{\sqrt{s}} \]
Find:
\[ g'(s) = \, ? \]
**Instructions:**
- Differentiate each term of the function \( g(s) \) with respect to \( s \).
- Apply the power rule, quotient rule, and chain rule as needed.
**Steps to Consider:**
1. The first term \( 9s^2 \) can be differentiated using the power rule.
2. The second term \( \frac{8}{s} \) is equivalent to \( 8s^{-1} \) and can be differentiated using the power rule.
3. The third term \( \frac{8}{\sqrt{s}} \) is equivalent to \( 8s^{-\frac{1}{2}} \) and can also be differentiated using the power rule.
**Complete the calculation to find \( g'(s) \).**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87946fbe-26a8-44e7-b719-4f36f43dcbac%2Fc0db38a0-ec1e-42fc-a1bb-1ea4083b49c0%2Fruq7otx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the derivative of the function.
Given:
\[ g(s) = 9s^2 - \frac{8}{s} + \frac{8}{\sqrt{s}} \]
Find:
\[ g'(s) = \, ? \]
**Instructions:**
- Differentiate each term of the function \( g(s) \) with respect to \( s \).
- Apply the power rule, quotient rule, and chain rule as needed.
**Steps to Consider:**
1. The first term \( 9s^2 \) can be differentiated using the power rule.
2. The second term \( \frac{8}{s} \) is equivalent to \( 8s^{-1} \) and can be differentiated using the power rule.
3. The third term \( \frac{8}{\sqrt{s}} \) is equivalent to \( 8s^{-\frac{1}{2}} \) and can also be differentiated using the power rule.
**Complete the calculation to find \( g'(s) \).**
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