dy as a function of x. Write the following function in the form y = f(u) and u = g(x). Then find xp 5x Write the given function in the form y = f(u) and u = g(x). Choose the correct answer below. O A. y=f(u) = u* and u = g(x) = + 5x - x? O B. y= f(u) = u and u = g(x) = - + 5x 3 OC. y= f(u) = u* and u = g(x) = x? 3 O D. y= f(u) = u and u = g(x) = - + 5x
dy as a function of x. Write the following function in the form y = f(u) and u = g(x). Then find xp 5x Write the given function in the form y = f(u) and u = g(x). Choose the correct answer below. O A. y=f(u) = u* and u = g(x) = + 5x - x? O B. y= f(u) = u and u = g(x) = - + 5x 3 OC. y= f(u) = u* and u = g(x) = x? 3 O D. y= f(u) = u and u = g(x) = - + 5x
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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Question
![The task is to write the given function in the form \( y = f(u) \) where \( u = g(x) \), and then find \(\frac{dy}{dx}\) as a function of \(x\).
The given function is:
\[ y = \left( \frac{x^2}{8} + 5x - \frac{3}{x} \right)^4 \]
The problem asks for the selection of the correct form from the multiple choices below:
**Options:**
A. \( y = f(u) = u^4 \) and \( u = g(x) = \left( \frac{x^2}{8} + 5x - \frac{3}{x} \right) \)
B. \( y = f(u) = u \) and \( u = g(x) = \frac{x^2}{8} + 5x \)
C. \( y = f(u) = u^4 \) and \( u = g(x) = \frac{x^2}{8} + 5x - \frac{3}{x} \)
D. \( y = f(u) = u \) and \( u = g(x) = \frac{x^2}{8} + 5x - \frac{3}{x} \)
---
**Explanation:**
The task involves selecting the correct expressions for \( y \) as a function of \( u \) and \( u \) as a function of \( x \) that match the initial given function structure. The correct answer should accurately represent the original function's form through these substitutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc7deb2c-0862-415e-88b2-023e0d274874%2F8dbc48d2-a29d-42db-a282-eabda64caf6a%2Fuqozalj_processed.png&w=3840&q=75)
Transcribed Image Text:The task is to write the given function in the form \( y = f(u) \) where \( u = g(x) \), and then find \(\frac{dy}{dx}\) as a function of \(x\).
The given function is:
\[ y = \left( \frac{x^2}{8} + 5x - \frac{3}{x} \right)^4 \]
The problem asks for the selection of the correct form from the multiple choices below:
**Options:**
A. \( y = f(u) = u^4 \) and \( u = g(x) = \left( \frac{x^2}{8} + 5x - \frac{3}{x} \right) \)
B. \( y = f(u) = u \) and \( u = g(x) = \frac{x^2}{8} + 5x \)
C. \( y = f(u) = u^4 \) and \( u = g(x) = \frac{x^2}{8} + 5x - \frac{3}{x} \)
D. \( y = f(u) = u \) and \( u = g(x) = \frac{x^2}{8} + 5x - \frac{3}{x} \)
---
**Explanation:**
The task involves selecting the correct expressions for \( y \) as a function of \( u \) and \( u \) as a function of \( x \) that match the initial given function structure. The correct answer should accurately represent the original function's form through these substitutions.
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