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Let f(x)=√4x² + 4x + 6 f'(x) = f'(5) =

Let f(x)=√4x² + 4x + 6 f'(x) = f'(5) =

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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### Educational Exercise: Derivatives #### Problem Statement Let \( f(x) = \sqrt{4x^2 + 4x + 6} \) - Find the derivative \( f'(x) \). - Calculate \( f'(5) \). #### Instructions 1. **Determine \( f'(x) \):** - Use the chain rule for derivatives. - Recall that the derivative of \(\sqrt{u}\) is \(\frac{1}{2\sqrt{u}} \times u'\), where \(u\) is the inner function. 2. **Calculate \( f'(5) \):** - Substitute \( x = 5 \) into your derived expression for \( f'(x) \). #### Notes - Ensure your answer is simplified as much as possible. - Check your calculations for accuracy.
Transcribed Image Text:### Educational Exercise: Derivatives #### Problem Statement Let \( f(x) = \sqrt{4x^2 + 4x + 6} \) - Find the derivative \( f'(x) \). - Calculate \( f'(5) \). #### Instructions 1. **Determine \( f'(x) \):** - Use the chain rule for derivatives. - Recall that the derivative of \(\sqrt{u}\) is \(\frac{1}{2\sqrt{u}} \times u'\), where \(u\) is the inner function. 2. **Calculate \( f'(5) \):** - Substitute \( x = 5 \) into your derived expression for \( f'(x) \). #### Notes - Ensure your answer is simplified as much as possible. - Check your calculations for accuracy.
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