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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![### Differential Calculus Exercise
**Problem Statement:**
Given the function
\[ f(x) = (x^3 + 5x + 8)^3 \]
Calculate the following:
1. The first derivative of the function, denoted as \( f'(x) \).
2. The value of the first derivative at \( x = 1 \), denoted as \( f'(1) \).
**Solution:**
1. **Finding \( f'(x) \):**
- Find the first derivative of the given function. You will need to apply the chain rule to differentiate the composite function.
\[ f'(x) = \]
2. **Finding \( f'(1) \):**
- Substitute \( x = 1 \) into the derivative function found in step 1.
\[ f'(1) = \]
By solving these calculations, you will derive the first derivative of the function and its value at \( x = 1 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e49950d-5fa0-4384-a169-4050fcaf3846%2F77b30166-bfd9-4ed3-8238-2558ed123d61%2F48n3pj8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Differential Calculus Exercise
**Problem Statement:**
Given the function
\[ f(x) = (x^3 + 5x + 8)^3 \]
Calculate the following:
1. The first derivative of the function, denoted as \( f'(x) \).
2. The value of the first derivative at \( x = 1 \), denoted as \( f'(1) \).
**Solution:**
1. **Finding \( f'(x) \):**
- Find the first derivative of the given function. You will need to apply the chain rule to differentiate the composite function.
\[ f'(x) = \]
2. **Finding \( f'(1) \):**
- Substitute \( x = 1 \) into the derivative function found in step 1.
\[ f'(1) = \]
By solving these calculations, you will derive the first derivative of the function and its value at \( x = 1 \).
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