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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![**Problem Statement**
Write the function in the form \( y = f(u) \) and \( u = g(x) \). Then find \( \frac{dy}{dx} \) as a function of \( x \).
Given:
\[ y = e^{-4x} \]
**Question**
Which of the following has the function in the form \( y = f(u) \) and \( u = g(x) \)?
A. \( y = e^u, \, u = -4x \)
B. \( y = -e^u, \, u = 4x \)
C. \( y = -4u, \, u = e^x \)
D. \( y = 4u, \, u = e^{-x} \)
**Task**
Find \( \frac{dy}{dx} \).
\[ \frac{dy}{dx} = \boxed{\phantom{answer}} \]
(Type an exact answer in terms of \( e \).)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc533774-2db2-4c40-ad62-e47c502b55d9%2F8830b274-8241-4660-86db-2a692df7147c%2Fkv5wrjp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement**
Write the function in the form \( y = f(u) \) and \( u = g(x) \). Then find \( \frac{dy}{dx} \) as a function of \( x \).
Given:
\[ y = e^{-4x} \]
**Question**
Which of the following has the function in the form \( y = f(u) \) and \( u = g(x) \)?
A. \( y = e^u, \, u = -4x \)
B. \( y = -e^u, \, u = 4x \)
C. \( y = -4u, \, u = e^x \)
D. \( y = 4u, \, u = e^{-x} \)
**Task**
Find \( \frac{dy}{dx} \).
\[ \frac{dy}{dx} = \boxed{\phantom{answer}} \]
(Type an exact answer in terms of \( e \).)
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