2. ( Quotient Rule, or Chain Rule. For others, you don't need anything more than Power Rule and three derivatives of basic functions (trig, e², and/or In(x)) and other basic properties of derivatives from 3.1. For some of these functions, it is NECESSARY to use at least one of Product Rule, For each question, NAME ALL RULES THAT ARE NECESSARY (Product Rule, Quotient Rule, Chain Rule) to find the derivative because it is impossible or extremely tedious to find the derivative without one of the rules. Write 'NO RULES' if you can find the derivative using only Power Rule and the derivatives of basic functions. Two examples are given. DO NOT COMPUTE ANY DERIVATIVES. Function ALL Rules Needed (Product, Quotient, and/or Chain) y == NO RULES sin(2) QUOTIENT RULE (11z² + 5)2 f(x) = V49+x² %3D y = (r+ 1)99 9(z) = V+2) VE %3D 7-1 h(t) = t³ V + t %3D sin(#/4) In(12)
2. ( Quotient Rule, or Chain Rule. For others, you don't need anything more than Power Rule and three derivatives of basic functions (trig, e², and/or In(x)) and other basic properties of derivatives from 3.1. For some of these functions, it is NECESSARY to use at least one of Product Rule, For each question, NAME ALL RULES THAT ARE NECESSARY (Product Rule, Quotient Rule, Chain Rule) to find the derivative because it is impossible or extremely tedious to find the derivative without one of the rules. Write 'NO RULES' if you can find the derivative using only Power Rule and the derivatives of basic functions. Two examples are given. DO NOT COMPUTE ANY DERIVATIVES. Function ALL Rules Needed (Product, Quotient, and/or Chain) y == NO RULES sin(2) QUOTIENT RULE (11z² + 5)2 f(x) = V49+x² %3D y = (r+ 1)99 9(z) = V+2) VE %3D 7-1 h(t) = t³ V + t %3D sin(#/4) In(12)
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...
Related questions
Topic Video
Question
![**Instructions for Derivative Rule Identification**
2. **[Instructor's Name]:** For some of these functions, it is necessary to use at least one of the Product Rule, Quotient Rule, or Chain Rule. For others, you don’t need anything more than the Power Rule and three derivatives of basic functions (trigonometric, exponential, and logarithmic functions) and other basic properties of derivatives from section 3.1.
For each question, **name all rules that are necessary** (Product Rule, Quotient Rule, Chain Rule) to find the derivative because it is impossible or extremely tedious to find the derivative without one of the rules. Write “NO RULES” if you can find the derivative using only the Power Rule and the derivatives of basic functions. Two examples are given.
**DO NOT COMPUTE ANY DERIVATIVES.**
| Function | All Rules Needed (Product, Quotient, and/or Chain) |
|----------|---------------------------------------------------|
| \( y = \frac{x}{x} \) | NO RULES |
| \( y = \frac{\sin(x)}{x} \) | QUOTIENT RULE |
| \( y = (11x^2 + 5)^2 \) | |
| \( f(x) = \sqrt{49 + x^2} \) | |
| \( y = (x + 1)^{99} \) | |
| \( g(x) = \frac{\sqrt{x^3 + x^2}}{\sqrt{x^2}} \) | |
| \( y = \frac{x^3 (e^x + 1)}{x - 1} \) | |
| \( h(t) = t^3 \sqrt{t^2 + t} \) | |
| \( y = \frac{e^5 \sin(\pi/4)}{\ln(12)} \) | |](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d5c52f5-eeda-4205-92ae-706134149552%2F18cbd06c-7bd8-4113-b486-31c430e653c9%2F6bb9poe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Instructions for Derivative Rule Identification**
2. **[Instructor's Name]:** For some of these functions, it is necessary to use at least one of the Product Rule, Quotient Rule, or Chain Rule. For others, you don’t need anything more than the Power Rule and three derivatives of basic functions (trigonometric, exponential, and logarithmic functions) and other basic properties of derivatives from section 3.1.
For each question, **name all rules that are necessary** (Product Rule, Quotient Rule, Chain Rule) to find the derivative because it is impossible or extremely tedious to find the derivative without one of the rules. Write “NO RULES” if you can find the derivative using only the Power Rule and the derivatives of basic functions. Two examples are given.
**DO NOT COMPUTE ANY DERIVATIVES.**
| Function | All Rules Needed (Product, Quotient, and/or Chain) |
|----------|---------------------------------------------------|
| \( y = \frac{x}{x} \) | NO RULES |
| \( y = \frac{\sin(x)}{x} \) | QUOTIENT RULE |
| \( y = (11x^2 + 5)^2 \) | |
| \( f(x) = \sqrt{49 + x^2} \) | |
| \( y = (x + 1)^{99} \) | |
| \( g(x) = \frac{\sqrt{x^3 + x^2}}{\sqrt{x^2}} \) | |
| \( y = \frac{x^3 (e^x + 1)}{x - 1} \) | |
| \( h(t) = t^3 \sqrt{t^2 + t} \) | |
| \( y = \frac{e^5 \sin(\pi/4)}{\ln(12)} \) | |
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning