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1 Find f'(x) for f(x) = %3D (x² - 9x)? f'(x) = Find f'(x) find f(x) = fo f'(x) = %3D Find f'(x) find f(x)= e 8x "(x) = %3D

1 Find f'(x) for f(x) = %3D (x² - 9x)? f'(x) = Find f'(x) find f(x) = fo f'(x) = %3D Find f'(x) find f(x)= e 8x "(x) = %3D

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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### Derivatives Exercise This exercise focuses on finding the derivative \( f'(x) \) for different functions \( f(x) \). 1. **Problem 17:** - **Function:** \( f(x) = \frac{1}{(x^2 - 9x)^2} \) - **Objective:** Find \( f'(x) \). - **Solution Placeholder:** \( f'(x) = \underline{\hspace{2cm}} \) 2. **Problem 18:** - **Function:** \( f(x) = e^{x^3} \) - **Objective:** Find \( f'(x) \). - **Solution Placeholder:** \( f'(x) = \underline{\hspace{2cm}} \) 3. **Problem 19:** - **Function:** \( f(x) = e^{8x} \) - **Objective:** Find \( f'(x) \). - **Solution Placeholder:** \( f'(x) = \underline{\hspace{2cm}} \) 4. **Problem 20:** - **Function:** \( f(x) = 4 e^{4x} \) - **Objective:** Find \( f'(x) \). - **Solution Placeholder:** \( f'(x) = \underline{\hspace{2cm}} \) ### Instructions: For each problem, use calculus techniques such as the chain rule and the power rule to find the derivatives. Fill in the solution placeholders with the correct expressions for \( f'(x) \). No graphs or diagrams are present in this exercise.
Transcribed Image Text:### Derivatives Exercise This exercise focuses on finding the derivative \( f'(x) \) for different functions \( f(x) \). 1. **Problem 17:** - **Function:** \( f(x) = \frac{1}{(x^2 - 9x)^2} \) - **Objective:** Find \( f'(x) \). - **Solution Placeholder:** \( f'(x) = \underline{\hspace{2cm}} \) 2. **Problem 18:** - **Function:** \( f(x) = e^{x^3} \) - **Objective:** Find \( f'(x) \). - **Solution Placeholder:** \( f'(x) = \underline{\hspace{2cm}} \) 3. **Problem 19:** - **Function:** \( f(x) = e^{8x} \) - **Objective:** Find \( f'(x) \). - **Solution Placeholder:** \( f'(x) = \underline{\hspace{2cm}} \) 4. **Problem 20:** - **Function:** \( f(x) = 4 e^{4x} \) - **Objective:** Find \( f'(x) \). - **Solution Placeholder:** \( f'(x) = \underline{\hspace{2cm}} \) ### Instructions: For each problem, use calculus techniques such as the chain rule and the power rule to find the derivatives. Fill in the solution placeholders with the correct expressions for \( f'(x) \). No graphs or diagrams are present in this exercise.
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