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If f(x) ƒ'(x) = 2 - x² 7+x² find:

If f(x) ƒ'(x) = 2 - x² 7+x² find:

Calculus: Early Transcendentals
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 6: Derivatives **Problem:** If \( f(x) = \frac{2 - x^2}{7 + x^2} \), find: \( f'(x) = \) **Instructions:** Calculate the derivative of the function \( f(x) \) given above. Fill in the derivative in the space provided. **Hints:** - Consider using the quotient rule for differentiation, which states: If \( f(x) = \frac{u(x)}{v(x)} \), then \( f'(x) = \frac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2} \). - Identify \( u(x) = 2 - x^2 \) and \( v(x) = 7 + x^2 \). **Solution Steps:** 1. Differentiate \( u(x) \) and \( v(x) \). 2. Substitute these into the quotient rule formula. 3. Simplify the expression to find \( f'(x) \).
Transcribed Image Text:### Question 6: Derivatives **Problem:** If \( f(x) = \frac{2 - x^2}{7 + x^2} \), find: \( f'(x) = \) **Instructions:** Calculate the derivative of the function \( f(x) \) given above. Fill in the derivative in the space provided. **Hints:** - Consider using the quotient rule for differentiation, which states: If \( f(x) = \frac{u(x)}{v(x)} \), then \( f'(x) = \frac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2} \). - Identify \( u(x) = 2 - x^2 \) and \( v(x) = 7 + x^2 \). **Solution Steps:** 1. Differentiate \( u(x) \) and \( v(x) \). 2. Substitute these into the quotient rule formula. 3. Simplify the expression to find \( f'(x) \).
Expert Solution
Step 1: Function value of f(x)

Given, f left parenthesis x right parenthesis equals fraction numerator 2 minus x squared over denominator 7 plus x squared end fraction

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