Consider the function. y = (2x² + 1)³ (a) Decompose the function in the form y = f(u) and u = g(x). (Use non-identity functions for f(u) and u.) {f(u), u} = dy (b) Find as a function of x. dx 12x (2x² + 1)² dy dx
Consider the function. y = (2x² + 1)³ (a) Decompose the function in the form y = f(u) and u = g(x). (Use non-identity functions for f(u) and u.) {f(u), u} = dy (b) Find as a function of x. dx 12x (2x² + 1)² dy 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
Consider the function:
\[ y = (2x^2 + 1)^3 \]
#### (a) Decomposition
Decompose the function in the form \( y = f(u) \) and \( u = g(x) \). Use non-identity functions for \( f(u) \) and \( u \).
\[ \{f(u), u\} = \{ \quad \} \text{ (Incorrect)} \]
#### (b) Differentiation
Find \(\frac{dy}{dx}\) as a function of \( x \).
\[ \frac{dy}{dx} = 12x(2x^2 + 1)^2 \]
The derivative is marked as correct.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4b64424-2f1e-400b-a2f3-ccc24d7d74e8%2Ff2a4ce14-447a-4d51-b150-5522c0e6e5c9%2Fv5g6etd_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Consider the function:
\[ y = (2x^2 + 1)^3 \]
#### (a) Decomposition
Decompose the function in the form \( y = f(u) \) and \( u = g(x) \). Use non-identity functions for \( f(u) \) and \( u \).
\[ \{f(u), u\} = \{ \quad \} \text{ (Incorrect)} \]
#### (b) Differentiation
Find \(\frac{dy}{dx}\) as a function of \( x \).
\[ \frac{dy}{dx} = 12x(2x^2 + 1)^2 \]
The derivative is marked as correct.
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