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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![### Calculus Problem: Derivatives
---
Given the function \( f(x) = (3x + 8)^{-4} \), find \( f'(x) \).
\[ f'(x) = \]
---
Next, find \( f'(1) \).
\[ f'(1) = \]
---
When solving this problem, you will apply the chain rule to differentiate the given function. The chain rule is essential for differentiating composites of functions. Let's break the solution down:
1. Identify the outer function and the inner function.
2. Differentiate the outer function with respect to the inner function.
3. Differentiate the inner function with respect to \( x \).
4. Combine the derivatives according to the chain rule formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f6b4032-4723-40f9-bafe-2ad74429fe12%2F9dc8660c-091f-4c14-8087-accfda19d229%2F5dbs6jc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculus Problem: Derivatives
---
Given the function \( f(x) = (3x + 8)^{-4} \), find \( f'(x) \).
\[ f'(x) = \]
---
Next, find \( f'(1) \).
\[ f'(1) = \]
---
When solving this problem, you will apply the chain rule to differentiate the given function. The chain rule is essential for differentiating composites of functions. Let's break the solution down:
1. Identify the outer function and the inner function.
2. Differentiate the outer function with respect to the inner function.
3. Differentiate the inner function with respect to \( x \).
4. Combine the derivatives according to the chain rule formula.
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