y = √/1+4x Part 1: Composition Express this function as a composition y = f(g(x)) of two simpler functions y = f(u) and u = g(x). 1. Identify the outer function (use variable "u"): Answer: f(u) = 2. Identify the inner function (use variable "x"): Answer: g(x) Part 2: Derivative 1. Apply the Chain Rule to calculate y'. Answer: y' = 2 x²
y = √/1+4x Part 1: Composition Express this function as a composition y = f(g(x)) of two simpler functions y = f(u) and u = g(x). 1. Identify the outer function (use variable "u"): Answer: f(u) = 2. Identify the inner function (use variable "x"): Answer: g(x) Part 2: Derivative 1. Apply the Chain Rule to calculate y'. Answer: y' = 2 x²
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
![We are going to calculate the derivative of the following function using the Chain Rule (or more specifically, the General Power Rule):
\[ y = \sqrt[3]{1 + 4x - x^2} \]
---
**Part 1: Composition**
Express this function as a composition \( y = f(g(x)) \) of two simpler functions \( y = f(u) \) and \( u = g(x) \).
1. Identify the outer function (use variable “\( u \)”):
Answer: \( f(u) = \) [______]
2. Identify the inner function (use variable “\( x \)”):
Answer: \( g(x) = \) [______]
---
**Part 2: Derivative**
1. Apply the Chain Rule to calculate \( y' \).
Answer: \( y' = \) [______]
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d728491-ca3a-470b-9076-be2816d1a071%2F44eb8a36-0286-4c8c-85bc-3432025793ac%2Ftqmwu4_processed.png&w=3840&q=75)
Transcribed Image Text:We are going to calculate the derivative of the following function using the Chain Rule (or more specifically, the General Power Rule):
\[ y = \sqrt[3]{1 + 4x - x^2} \]
---
**Part 1: Composition**
Express this function as a composition \( y = f(g(x)) \) of two simpler functions \( y = f(u) \) and \( u = g(x) \).
1. Identify the outer function (use variable “\( u \)”):
Answer: \( f(u) = \) [______]
2. Identify the inner function (use variable “\( x \)”):
Answer: \( g(x) = \) [______]
---
**Part 2: Derivative**
1. Apply the Chain Rule to calculate \( y' \).
Answer: \( y' = \) [______]
---
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