If f(x) = (3x + 8), find f'(x). %3D Find f'(1).

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.
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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