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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![**Instruction: Use the table to the right to find the given derivative.**
\[
\frac{d}{dx} \left[ f(x)g(x) \right]_{x=5}
\]
---
**Answer:**
\[
\frac{d}{dx} \left[ \frac{f(x)}{g(x)} \right]_{x=5} = \_\_\_ \quad (\text{Simplify your answer.})
\]
---
**Table:**
\[
\begin{array}{c|c|c|c|c|c}
x & 1 & 2 & 3 & 4 & 5 \\
\hline
f(x) & 4 & 2 & 5 & 3 & 1 \\
f'(x) & 2 & 5 & 4 & 3 & 1 \\
g(x) & 2 & 5 & 4 & 3 & 1 \\
g'(x) & 5 & 4 & 3 & 1 & 2 \\
\end{array}
\]
**Explanation:**
- The problem involves finding derivatives using given values.
- The table provides values of functions \( f(x) \), \( g(x) \) and their derivatives \( f'(x) \), \( g'(x) \) at specific points \( x = 1, 2, 3, 4, \text{and } 5 \).
- Use these values to perform derivative calculations at \( x = 5 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65e9754d-e7bf-4951-a913-18b478a6d2d4%2Fb230f4a0-f8de-4f69-b6f6-9eb90a1ac7c9%2F1o5mlho_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Instruction: Use the table to the right to find the given derivative.**
\[
\frac{d}{dx} \left[ f(x)g(x) \right]_{x=5}
\]
---
**Answer:**
\[
\frac{d}{dx} \left[ \frac{f(x)}{g(x)} \right]_{x=5} = \_\_\_ \quad (\text{Simplify your answer.})
\]
---
**Table:**
\[
\begin{array}{c|c|c|c|c|c}
x & 1 & 2 & 3 & 4 & 5 \\
\hline
f(x) & 4 & 2 & 5 & 3 & 1 \\
f'(x) & 2 & 5 & 4 & 3 & 1 \\
g(x) & 2 & 5 & 4 & 3 & 1 \\
g'(x) & 5 & 4 & 3 & 1 & 2 \\
\end{array}
\]
**Explanation:**
- The problem involves finding derivatives using given values.
- The table provides values of functions \( f(x) \), \( g(x) \) and their derivatives \( f'(x) \), \( g'(x) \) at specific points \( x = 1, 2, 3, 4, \text{and } 5 \).
- Use these values to perform derivative calculations at \( x = 5 \).
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