dy as a function of x. Write the function in the form y = f(u) and u= g(x). Then find y = (- 2x +8) dy O A. y=u3; u = - 2x + 8; = - 6(- 2x + 8)2 dx dy O B. y= u; u= - 2x + 8; dx = 3(- 2x + 8)? dy Oc. y=u3; u= - 2x +8; - 2(- 2x + 8)3 dx = dy O D. y= 3u + 8; u = x; - 6x2 dx
dy as a function of x. Write the function in the form y = f(u) and u= g(x). Then find y = (- 2x +8) dy O A. y=u3; u = - 2x + 8; = - 6(- 2x + 8)2 dx dy O B. y= u; u= - 2x + 8; dx = 3(- 2x + 8)? dy Oc. y=u3; u= - 2x +8; - 2(- 2x + 8)3 dx = dy O D. y= 3u + 8; u = x; - 6x2 dx
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 \(x\).
\[ y = (-2x + 8)^3 \]
**Options:**
- **Option A:**
\( y = u^3; \, u = -2x + 8; \, \frac{dy}{dx} = -6(-2x + 8)^2 \)
- **Option B:**
\( y = u^3; \, u = -2x + 8; \, \frac{dy}{dx} = 3(-2x + 8)^2 \)
- **Option C:**
\( y = u^3; \, u = -2x + 8; \, \frac{dy}{dx} = -2(-2x + 8)^3 \)
- **Option D:**
\( y = 3u + 8; \, u = x^3; \, \frac{dy}{dx} = -6x^2 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65e9754d-e7bf-4951-a913-18b478a6d2d4%2F63b04498-2a01-44c3-9b44-6be0abdf25de%2F4haswj_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 \(x\).
\[ y = (-2x + 8)^3 \]
**Options:**
- **Option A:**
\( y = u^3; \, u = -2x + 8; \, \frac{dy}{dx} = -6(-2x + 8)^2 \)
- **Option B:**
\( y = u^3; \, u = -2x + 8; \, \frac{dy}{dx} = 3(-2x + 8)^2 \)
- **Option C:**
\( y = u^3; \, u = -2x + 8; \, \frac{dy}{dx} = -2(-2x + 8)^3 \)
- **Option D:**
\( y = 3u + 8; \, u = x^3; \, \frac{dy}{dx} = -6x^2 \)
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