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Problem

If $ F(x) = f(g(x)), $ where $ f(-2) = 8, f'(-2) …

01:10

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Problem 60 Hard Difficulty

At what point on the curve $ y = \sqrt {1 + 2x} $ is the tangent line perpendicular to the line $ 6x + 2y = 1? $


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01:10

Frank Lin

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Related Topics

Derivatives

Differentiation

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Chanse S.

November 15, 2020

Thank you!! You teach at Oregon State?

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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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Watch More Solved Questions in Chapter 3

Problem 1
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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
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Problem 32
Problem 33
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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
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Problem 64
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Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
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Problem 82
Problem 83
Problem 84
Problem 85
Problem 86
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Problem 88
Problem 89
Problem 90
Problem 91
Problem 92
Problem 93
Problem 94
Problem 95
Problem 96
Problem 97
Problem 98
Problem 99
Problem 100

Video Transcript

in this problem. We're looking for the point where the Tanja line is perpendicular to the given line and perpendicular lines have opposite reciprocal slopes. So let's find the slope of the given line. Let's take this equation and isolate why. So we'll subtract six x from both sides and divide by two. So the slope of this line is negative. Three. So the perpendicular slope would be positive 1/3. So we're looking for the point where the Tanja line has a slope of 1/3. That means we want the derivative to equal 1/3. So let's find the derivative. I'm going to rewrite the function as one plus two x to the 1/2 power and then I'm going to use the chain rule. Why Prime equals 1/2 times one plus two x to the negative 1/2 power that takes care of the first part of the chain rule times the derivative of the inside, which is to now we can multiply the 1/2 of the two that was canceled. And now we want this derivative to be equal to 1/3 so this derivative could be written as one over the square root of one plus two x, and it equals 1/3. Let's take the reciprocal of both sides, and we have a square root of one plus two. X is equal to three. Now it's square both sides, and we have one plus two. X equals nine. Subtract 12 X equals eight and divide by two. X equals four. Okay, this is the X coordinate of the point. We also want the Y coordinate of the point, and the Y coordinate would be what we get when we take four and substituted into the original equation. So we have one plus two times for inside a square root square root of nine is three. So the point we're looking for is the 0.0.43

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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.

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