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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
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 \( x = 1 \)
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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