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

A table of values for $ f, g, f' , $ and $ g' $ is given.(a) If $ h(x) = f(g(x)), $ find $ h'(1). $(b) If $ H(x) = g(g(x)), $ find $ H(1). $

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

01:00

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Oregon State University

Baylor University

University of Nottingham

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.

0:00

A table of values for $f, …

05:32

A table of values for f, g…

02:38

A table of values for $f ,…

01:45

01:46

01:21

Find $f \circ g \circ h$

01:31

Find $f(x)$ and $g(x)$ so …

01:34

Find functions $f$ and $g$…

01:37

03:28

For each pair of functions…

02:10

If $f(x)=x^{2}+1, g(x)=\fr…

02:09

For the following exercise…

01:54

If $f(x)=4 x, g(x)=2 x-1,$…

for party This problem we want to find aged prime of one and we know that h of x is f of G of X. So let's use the chain rule to find h prime at X h. Prime of X will be the derivative of the outside f prime of Jew vex times the derivative of the inside G prime of X. Now let's substitute one in their h prime of one will be f prime of G of one times g prime of one. Now we can refer to the table g of one is to and g prime of one is six so we can substitute those numbers in so h prime of one is f prime of to times six. Now we need to find f prime of to looking at the table f prime of two is five so we have five times six So the answer is 30 And for part B, we're finding h prime of one for capital H and capital H is g of f of X. So the derivative of capital age according to the chain rule will be the derivative of the outside G prime of f of X times a derivative of the inside F prime of X. So now let's evaluate that at one h prime of one will be G prime of F one times f prime of one. Now let's use the table to find f of one and effort one is three and f prime of one f prime of one is for. So let's substitute those numbers in and we have aged. Prime of one equals G prime of three times four. Now let's find you a prime of three. J Prime of three is nine. So let's substitute that in and we have nine times for so our answer is 36.

View More Answers From This Book

Find Another Textbook

03:08

'Problem Z: Unemployment Benefits The average weekly unemployment benef…

01:40

'5. Find the measures of the angles between diagonals of a rectangle wh…

01:24

'The function; P, gives the cost (in dollars to fix the road in terms o…

06:30

"16. Selecting a State Choose one of the 50 states at random; What is t…

'y" _ 2y = 0, y(0) = 2, y (0)'

01:06

'Assume that randomly selected subject is given bone density test Those…

02:45

'4_ Solve the following initial value problems using the method of Lapl…

04:48

'EXAMPLE 2 Exponential Growth Cholera; intestinal disease is caused by …

04:05

'In a single channel automatic car wash , cars arrive following Poisson…

03:07

'In your classroom there are 45 students assume that none of them is bo…