Problem

If $ f(x) = \sin x + \ln x, $ find $ f'(x). $ Che…

01:02

Problem 34 Easy Difficulty

Find an equation of the tangent line to the curve at the given point.

$ y = x^2 \ln x, (1, 0) $

Answer

$y=x-1$

Watch More Solved Questions in Chapter 3

Problem 1

Problem 2

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Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

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Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

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Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

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Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

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Problem 39

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Problem 42

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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

in this problem, we have to find the equation for the tangent line to a curve and specifically were given a curve that is defined by a log rhythmic function. So we have the function. Why equals X square times the natural log of X and what we need to do before we confined the tangent line is find my prime. Well, how do we do that? We're going to have to apply the product rule. So why Prime would be equal to d X square dx times the national log of X plus x squared times d natural log of X over d x So when you do that, we simplify just a little bit. We get why prime equals two x times the natural log of X plus x So we have the derivative. But we want to know the equation for the tangent line. So what do we have to do now? We need the slope of our tangent line at the point that we're told in the problem 10 so we can plug in our X value into y prime. So why prime would be equal to two times one times the natural log of one plus one, so we would get zero plus one, which equals one. And now we confined the tangent line very easily. We have this form. Why? Minus why not equals M times X minus X not. And then we could just plug in the X and Y coordinates from our point, so we would have y minus zero equals one times X minus one, and then we can simplify to get the tangent line equals Why equal toe X negative one x minus one. Excuse me. So I hope that this problem helped you understand how we can find the tangent line to a curb using differentiation, specifically finding the derivative of a of a logarithmic function.

Madi S.

University of Denver

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 6

Derivatives of Logarithmic Functions

Problem

If $ f(x) = \sin x + \ln x, $ find $ f'(x). $ Che…

Problem 34 Easy Difficulty

Find an equation of the tangent line to the curve at the given point.

$ y = x^2 \ln x, (1, 0) $

Answer

$y=x-1$

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Calculus: Early Transcendentals

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