Problem

Differentiate the function. $ y = \ln (\csc x …

01:58

Question

Answered step-by-step

Problem 17 Easy Difficulty

Differentiate the function.

$ T(z) = 2^z \log_2 z $

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Carson Merrill

Numerade Educator

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

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

Video Transcript

So for this problem, we're learning essentially how to take the derivatives of logarithmic functions. So what we're starting off in this case is a function t of Z. And it doesn't matter how we write this weaken right as TMZ ffx whatever, because just a function. Um but in this case, what we'll have is t of Z being equal to too busy times log based too, Zeke. So we're gonna want to use what's known as the product group for differentiation and how that's gonna look is we take the derivative of the first term that we're multiplying by. So to to the Z, we know that, uh, the derivative of to To the Z is going to be to To the Z I'm the natural log of to and then that will be multiplied by just log based too busy. We don't have to differentiate that at first. And then we add that with two to the scene times the derivative of this portion right here we know that the derivative of logarithmic function is going to be one over the U value. In this case, that would be easy times the natural log of the base value, which is to So that should be our answer right here. Then what we can do is simplify things further. You could either factor out the two Z. Um, that's one option or another thing that can be done is, um, simplifying things further. If we view this right here as the natural log of Z over the natural log of too, that's another way you could write it. If we do that, then this will cancel with this right here. Eso we would have that and then we can write to to the Z up top here. So this would be our final, um, mawr simplified form of it. We could also factor out of Tuesday if we wanted to. It would be too, too busy times natural log of Z plus one over z times, the natural rate of two. However, this could be an easier way of writing it. And then if we had t prime of Z, we would end up getting this exact same graph. Um but yeah, this ultimately just shows us how to dio a better job of differentiating logarithmic functions, which is crucial when dealing with applications of math which use a lot of rhythmic functions all the time.

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.

Problem

Differentiate the function. $ y = \ln (\csc x …

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

More Answers

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 1 / AB Educators

Grace He

Heather Zimmers

Kayleah Tsai

Michael Jacobsen

Calculus 1 / AB Courses

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript

James Stewart

Calculus: Early Transcendentals

Grace He

Caleb Elmore

Samuel Hannah

Michael Jacobsen

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

Calculus: Early Transcendentals

Grace He

Heather Zimmers

Kayleah Tsai

Michael Jacobsen

James StewartCalculus: Early Transcendentals

Grace He

Caleb Elmore

Samuel Hannah

Michael Jacobsen

James Stewart

Calculus: Early Transcendentals