Let h(x) = f(g(x)) and p(x) = g(f(x)). Use the table below to compute the following derivatives. a. h'(4) b. p'(1) X 1 f(x) 1 f'(x) -7 g(x) g'(x) 437 24 41-T7 ܚ ܚ ܝ ܚ ܗ |ܙܢ -8 43 1 2 4 7
Let h(x) = f(g(x)) and p(x) = g(f(x)). Use the table below to compute the following derivatives. a. h'(4) b. p'(1) X 1 f(x) 1 f'(x) -7 g(x) g'(x) 437 24 41-T7 ܚ ܚ ܝ ܚ ܗ |ܙܢ -8 43 1 2 4 7
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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![**Homework: Homework 3.7**
**Problem Statement:**
Let \( h(x) = f(g(x)) \) and \( p(x) = g(f(x)) \). Use the table below to compute the following derivatives:
a. \( h'(4) \)
b. \( p'(1) \)
**Table:**
| \( x \) | \( f(x) \) | \( f'(x) \) | \( g(x) \) | \( g'(x) \) |
|:------:|:---------:|:----------:|:---------:|:----------:|
| 1 | 1 | -7 | 4 | 3 |
| 2 | 4 | -4 | 1 | 1 |
| 3 | 2 | -8 | 3 | 5 |
| 4 | 3 | -1 | 2 | 4 |
**Instructions:**
1. To find \( h'(4) \):
- Use the chain rule: \( h'(x) = f'(g(x)) \cdot g'(x) \)
- Substitute \( x = 4 \)
2. To find \( p'(1) \):
- Use the chain rule: \( p'(x) = g'(f(x)) \cdot f'(x) \)
- Substitute \( x = 1 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa204fb01-1593-427c-b210-f132b42420bd%2Ff6fb997b-571c-4d1b-9b2d-6ce8138ffef0%2Fjajdhul_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Homework: Homework 3.7**
**Problem Statement:**
Let \( h(x) = f(g(x)) \) and \( p(x) = g(f(x)) \). Use the table below to compute the following derivatives:
a. \( h'(4) \)
b. \( p'(1) \)
**Table:**
| \( x \) | \( f(x) \) | \( f'(x) \) | \( g(x) \) | \( g'(x) \) |
|:------:|:---------:|:----------:|:---------:|:----------:|
| 1 | 1 | -7 | 4 | 3 |
| 2 | 4 | -4 | 1 | 1 |
| 3 | 2 | -8 | 3 | 5 |
| 4 | 3 | -1 | 2 | 4 |
**Instructions:**
1. To find \( h'(4) \):
- Use the chain rule: \( h'(x) = f'(g(x)) \cdot g'(x) \)
- Substitute \( x = 4 \)
2. To find \( p'(1) \):
- Use the chain rule: \( p'(x) = g'(f(x)) \cdot f'(x) \)
- Substitute \( x = 1 \)
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