Find the following using the table below. X f(x) f'(x) 4 g(x) 1 1 2 3 4 1 2 3 4 2 3 1 4 3 2 ال لا 4 1 2 3 h'(4) if h(x) = f(x) · g(x) f(x) g(x) h'(4) if h(x) = f(g(x)) h'(4) if h(x) = > Next Question

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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b
Find the following using the table below.
3 4
3
4
1
1 4 3 2
1 2
X
1
f(x) 1
g(x)
g'(x) 4
22
4 2 3
2
h'(4) if h(x)=
3
لیا
h'(4) if h(x) = f(x) · g(x)
f(x)
g(x)
h'(4) if h(x) = f(g(x))
> Next Question
Transcribed Image Text:b Find the following using the table below. 3 4 3 4 1 1 4 3 2 1 2 X 1 f(x) 1 g(x) g'(x) 4 22 4 2 3 2 h'(4) if h(x)= 3 لیا h'(4) if h(x) = f(x) · g(x) f(x) g(x) h'(4) if h(x) = f(g(x)) > Next Question
Expert Solution
Step 1: Define the Product Rule, the Quotient Rule, the Chain Rule:

The Product Rule:

open parentheses f times g close parentheses to the power of apostrophe equals f apostrophe times g plus f times g apostrophe

The Quotient Rule:

open parentheses f over g close parentheses to the power of apostrophe equals fraction numerator f apostrophe times g minus g apostrophe times f over denominator g squared end fraction

The Chain Rule:

open square brackets f open parentheses g open parentheses x close parentheses close parentheses close square brackets to the power of apostrophe equals f apostrophe open parentheses g open parentheses x close parentheses close parentheses times g apostrophe open parentheses x close parentheses

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