Download the App!

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

Question

Answered step-by-step

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

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Heather Zimmers

Numerade Educator

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

00:32

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Yang L.

March 31, 2021

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

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

04:40

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.

44:57

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.

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

01:09

02:18

Let fand g be differentiab…

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.

View More Answers From This Book

Find Another Textbook

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, thenJul? +2u.v + Iv/?