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 Statement:**
For each of \( h(x) \), find \( h'(x) \):
**(a)** \( h_1(x) = \frac{x^2}{x^3+2} \). Hint: Use Quotient Rule.
**Explanation for Educational Use:**
To find the derivative of a function given as a quotient of two functions, you can apply the Quotient Rule. The Quotient Rule states that if you have a function \( h(x) = \frac{f(x)}{g(x)} \), then its derivative \( h'(x) \) is given by:
\[
h'(x) = \frac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2}
\]
In this problem, identify:
- \( f(x) = x^2 \)
- \( g(x) = x^3 + 2 \)
Use the Quotient Rule to find \( h'(x) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb234898a-ca00-4740-ae3d-79576f672843%2F960929b4-6396-4210-a0a3-5a18f3f611d8%2F6eptzwn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
For each of \( h(x) \), find \( h'(x) \):
**(a)** \( h_1(x) = \frac{x^2}{x^3+2} \). Hint: Use Quotient Rule.
**Explanation for Educational Use:**
To find the derivative of a function given as a quotient of two functions, you can apply the Quotient Rule. The Quotient Rule states that if you have a function \( h(x) = \frac{f(x)}{g(x)} \), then its derivative \( h'(x) \) is given by:
\[
h'(x) = \frac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2}
\]
In this problem, identify:
- \( f(x) = x^2 \)
- \( g(x) = x^3 + 2 \)
Use the Quotient Rule to find \( h'(x) \).
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