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Problem

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Problem 43 Hard Difficulty

Find the points on the lemniscate in Exercise 31 where the tangent is horizontal.


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Doruk Isik
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00:57

Frank Lin

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Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

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Derivatives

Differentiation

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Derivatives - Intro

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.

Video Thumbnail

44:57

Differentiation Rules - Overview

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.

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Problem 1
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Problem 5
Problem 6
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 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
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80

Video Transcript

in this problem where us to use the question given in exercise regularly and west find the ordinance off the present attention. So basically, we first need to the French Air Destructor X. Let's do that. We have four times. Expert Buzz Weisberg, Times David Talked Inter function, which is to eggs waas to our times y prime physical to 25 times two X minus two. Why crime? All right, we know that, uh, tension lines were gentle. One before Stuart zero. So let's set what 00.0 we have, then four times. Expect for spirit Times two X is equal to 25 times two x From this, we got any questions off a form to x times four times x great plus y squared minus 25. Physical zero. Now we want this to hold. It means that this should be zero. So this will give us a relationship between exit. Why we have ex scraped bus. Weisberg is equal to 25 or four. Now let's say that this is our question them to end. The orginal main question is a question or, um, because you could use any old one punch and silver using want and to so using one and two. We see that Why could be positive. Negative plus minus four. Why is this? We can use question number. Judy Clark X. We have Expert is equal to 25 44 minus y spirit. So the name described is 25 4 uh, minus 25 for 16 that iss 75 over 16. So this means that X could be plus by this five scourge on +34 Combining these two, we find accordance as post minus fire. Um, Skurdal three over four plus minus five over four.

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Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Caleb Elmore

Baylor University

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

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.

Video Thumbnail

44:57

Differentiation Rules - Overview

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.

Join Course
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