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
determine the fourth derivative of the given function (number 9)
![### Calculus Problem Set
The following are exercises involving differentiation and function analysis. Specifically, they require finding derivatives, with a focus on calculating the second derivative for problems 10 to 20.
---
**Problem 7:**
\[ y = 9\sin(z) - \sin(4z) + 7\cos\left(\frac{2z}{3}\right) \]
**Problem 8:**
\[ R(x) = 2e^{-x} - 3e^{1+8x} + 9\ln(6x) \]
**Problem 9:**
\[ f(t) = \ln(t^6) - \cos(4t) + 9\sin(2t) + e^{7t} \]
**For problems 10 to 20, determine the second derivative.**
**Problem 10:**
\[ Q(w) = \cos(2 - 7w^2) \]
**Problem 11:**
\[ f(z) = \sin(1 + e^{2x}) \]
**Problem 12:**
\[ y = \tan(3x) \]
**Problem 13:**
\[ z = \csc(8w) \]
**Problem 14:**
\[ f(u) = e^{4u^2 + 9u} \]
---
Use these exercises to practice skills in calculus, particularly focusing on the rules of differentiation such as the chain rule, product rule, and quotient rule.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F237d4048-a709-45b4-bafb-64f7e9c62b1d%2Fa25a51bb-b646-41bd-8048-38d8c696d15f%2Fota9z39.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculus Problem Set
The following are exercises involving differentiation and function analysis. Specifically, they require finding derivatives, with a focus on calculating the second derivative for problems 10 to 20.
---
**Problem 7:**
\[ y = 9\sin(z) - \sin(4z) + 7\cos\left(\frac{2z}{3}\right) \]
**Problem 8:**
\[ R(x) = 2e^{-x} - 3e^{1+8x} + 9\ln(6x) \]
**Problem 9:**
\[ f(t) = \ln(t^6) - \cos(4t) + 9\sin(2t) + e^{7t} \]
**For problems 10 to 20, determine the second derivative.**
**Problem 10:**
\[ Q(w) = \cos(2 - 7w^2) \]
**Problem 11:**
\[ f(z) = \sin(1 + e^{2x}) \]
**Problem 12:**
\[ y = \tan(3x) \]
**Problem 13:**
\[ z = \csc(8w) \]
**Problem 14:**
\[ f(u) = e^{4u^2 + 9u} \]
---
Use these exercises to practice skills in calculus, particularly focusing on the rules of differentiation such as the chain rule, product rule, and quotient rule.
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