Use the table to find the following derivatives: f(x) -3 g(x) 2 f'(x) -5 -1 g'(x) 7 4 2 8. This question has multiple parts: 1. d. dx f (x), I=2 55 160 440 22 314 225
Use the table to find the following derivatives: f(x) -3 g(x) 2 f'(x) -5 -1 g'(x) 7 4 2 8. This question has multiple parts: 1. d. dx f (x), I=2 55 160 440 22 314 225
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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![### Use the table to find the following derivatives:
| \( x \) | 1 | 2 | 3 | 4 | 5 |
|---------|---|---|---|---|---|
| \( f(x) \) | -3 | -2 | 1 | 4 | 5 |
| \( g(x) \) | 2 | 5 | 4 | 0 | 1 |
| \( f'(x) \) | -5 | -1 | 4 | 2 | 6 |
| \( g'(x) \) | 7 | 1 | 6 | 2 | 8 |
---
### This question has multiple parts:
1. Calculate the following derivative at \( x = 2 \):
\[
\frac{d}{dx} \left( x^5 \cdot f(x) \right)
\]
2. Calculate the following derivative at \( x = 1 \):
\[
\frac{d}{dx} \left( \frac{g(x)}{2x} \right)
\]
3. Calculate the following derivative at \( x = 4 \):
\[
\frac{d}{dx} \left( g \left( f(x) \right) [?][?] \right)
\]
(Note: The question marks indicate incomplete information that requires clarification.)
---
Ensure you apply the appropriate rules for differentiation, such as the product rule, quotient rule, and chain rule, where necessary. Use the values provided in the table for the calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4e3da8d7-5e45-4b35-92f7-ecdb5bd91ee7%2Fd4052d18-e089-4821-aed7-599102326247%2Fy3sxxo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Use the table to find the following derivatives:
| \( x \) | 1 | 2 | 3 | 4 | 5 |
|---------|---|---|---|---|---|
| \( f(x) \) | -3 | -2 | 1 | 4 | 5 |
| \( g(x) \) | 2 | 5 | 4 | 0 | 1 |
| \( f'(x) \) | -5 | -1 | 4 | 2 | 6 |
| \( g'(x) \) | 7 | 1 | 6 | 2 | 8 |
---
### This question has multiple parts:
1. Calculate the following derivative at \( x = 2 \):
\[
\frac{d}{dx} \left( x^5 \cdot f(x) \right)
\]
2. Calculate the following derivative at \( x = 1 \):
\[
\frac{d}{dx} \left( \frac{g(x)}{2x} \right)
\]
3. Calculate the following derivative at \( x = 4 \):
\[
\frac{d}{dx} \left( g \left( f(x) \right) [?][?] \right)
\]
(Note: The question marks indicate incomplete information that requires clarification.)
---
Ensure you apply the appropriate rules for differentiation, such as the product rule, quotient rule, and chain rule, where necessary. Use the values provided in the table for the calculations.
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