Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Let $ g(x) = e^{\alpha} + f(x) $ and $ h(x) = e^{…

05:02

Question

Answered step-by-step

Problem 69 Medium Difficulty

Suppose $ f $ is differentiable on $ \mathbb{R}. $ Let $ F(x) = f(e^x) $ and $ G(x) = e^{f(x)}. $ Find expressions for
(a) $ F'(x) $ (b) $ G'(x). $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Heather Zimmers
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Heather Zimmers

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

00:32

Frank Lin

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Related Topics

Derivatives

Differentiation

Discussion

You must be signed in to discuss.
YL

Yang L.

March 31, 2021

(a) Find the differential dy. y = 1 x + 2

Top Calculus 1 / AB Educators
Catherine Ross

Missouri State University

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Michael Jacobsen

Idaho State University

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
Recommended Videos

01:22

Suppose $ f $ is different…

02:10

Suppose $F(x)=f(x) / x,$ w…

01:30

Suppose f is differentiabl…

01:48

Let $f$ and $g$ be differe…

03:06

Suppose $F(x)=x^{3} f(x),$…

01:13

Let $f$ and $g$ be differe…

01:09

Let $f$ and $g$ be differe…

02:18

Let fand g be differentiab…

Watch More Solved Questions in Chapter 3

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84
Problem 85
Problem 86
Problem 87
Problem 88
Problem 89
Problem 90
Problem 91
Problem 92
Problem 93
Problem 94
Problem 95
Problem 96
Problem 97
Problem 98
Problem 99
Problem 100

Video Transcript

here we have capital F of X, which is a composite function with little F as the outside function and eat of the X as the inside function. So it's derivative. Using the chain rule would be the derivative of the outside F prime of E to the X Times, the derivative of the inside E to the X. And then we have capital G of X, also a composite function. It's outside function is the each of the X function and it's inside. Function is f of X, so it's derivative would be the derivative of the outside e to the f of x times, the derivative of the inside F prime of X.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
84
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
53
Hosted by: Alonso M
See More

Related Topics

Derivatives

Differentiation

Top Calculus 1 / AB Educators
Catherine Ross

Missouri State University

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Michael Jacobsen

Idaho State University

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
Recommended Videos

01:22

Suppose $ f $ is differentiable on $ \mathbb{R}. $ Let $ F(x) = f(e^x) $ and $ …

02:10

Suppose $F(x)=f(x) / x,$ where $f$ is a differentiable function. Find $F^{\prim…

01:30

Suppose f is differentiable on R, Let F(x) f(eX) and G(x) eflx) _ (a) Find an e…

01:48

Let $f$ and $g$ be differentiable functions such that $f^{\prime}(x)=$ $g(x)$ a…

03:06

Suppose $F(x)=x^{3} f(x),$ where $f$ is a differentiable function. Find $F^{\pr…

01:13

Let $f$ and $g$ be differentiable functions such that $f^{\prime}(x)=$ $g(x)$ a…

01:09

Let $f$ and $g$ be differentiable functions such that $f^{\prime}(x)=$ $g(x)$ a…

02:18

Let fand g be differentiable functions with the following properties: g(x) > 0 …
Additional Mathematics Questions

03:04

Player runs t0 first base at speed of 20 fts while Player runs from second b…

02:33

A population of animals oscillates yearly between low of 1300 on January Ist…

01:37

Suppose we want to predict the probability of rain on a day; given the perce…

01:55

A mirror is the shape of an ellipse defined by =1 with units in feet. Which …

03:21

3.5 Coin flips: If you flip a fair coin 10 times, what is the probability of…

01:02

The following curve is to be a density curve for & random variable X Wha…

03:13

and g(x) = find the following composite functions and state the domain of ea…

02:19

Market research was performed on 1000 visitors to shopping mall who particip…

01:44

The fox population in certain region has an annual growth rate of 4 percent …

02:55

38. Show' that ifu and are vectors, then
Jul? +2u.v + Iv/?

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started