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

Let $ f $ and $ g $ be the function in Exercise 63.(a) If $ F(x) = f(f(x)), $ find $ F'(2). $(b) If $ G(x) = g(g(x)), $ find $ G'(3). $

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

00:57

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Missouri State University

Campbell University

Harvey Mudd College

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.

02:00

Let $f$ and $g$ be the fun…

01:20

0:00

01:02

Find $g \circ f$ and $f^{\…

03:56

Let f and g be the functio…

01:08

For the given functions an…

02:02

If $f(x)=\left(a x^{2}+b\r…

01:09

For the functions $f$ and …

02:01

01:14

02:55

01:54

in this problem. Capital F of X is f of f of X and we want to find capital f prime of to. So let's find capital f prime of X using the chain rule The derivative of the outside would be f prime of f of x times, the derivative of the inside F prime of X. Now let's evaluate that at two. So capital F prime of two would be f prime of f of to times f prime of to Now we use the table to find f of to f of two is one and f prime of to if prime of two is five and we substitute those numbers in So we have f prime of one times five. Now we go back to the table to find f prime of one of prime of oneness four Suite four times five. So the answer is 20. And for part B, we have capital G FX, which is G of G of X and we want to find capital G prime of three. So let's find capital G prime of X using the chain rule. The derivative of the outside would be g prime of G of X Times, the derivative of the inside G prime of X. Now let's evaluate that at three. So G prime of three would be g prime of G of three times g Prime of three. Now let's use the table to find G of three. G of three is too. And to find g prime of three g Prime of three is nine so we can substitute those values in and we get G prime of to times nine. Now we can look back at the table for G Prime of two g Prime of two is seven to have seven times nine, so the answer is 63.

View More Answers From This Book

Find Another Textbook

04:10

A medieval city has the shape of a square and is protected by walls with len…

06:05

A ball is thrown eastward into the air from the origin (in the direction of …

02:14

Find the differential of the function.$L=x z e^{-y^{2}-z^{2}}$

02:23

If $V(x, y)$ is the electric potential at a point $(x, y)$ in the $x y$ -pla…

03:13

Each of these extreme value problems has a solution with both a maximum valu…

03:50

Level curves for barometric pressure (in millibars) are shown for $6: 00 \ma…

04:03

Find the maximum rate of change of $f$ at the given point and the direction …

05:05

If $f(x, y)=\sqrt[3]{x^{3}+y^{3}},$ find $f_{x}(0,0)$

03:34

Set up the triple integral of an arbitrary continuous function $f(x, y, z)$ …

02:51

Match the vector fields $F$ with the plots labeled I-IV. Give reasons for yo…