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Problem

Find the derivative of the function. $ F(t) = \f…
02:36

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Problem 31 Easy Difficulty

Find the derivative of the function.
$ F(t) = e^{t \sin 2t} $

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00:32

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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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.
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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
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
Problem 81
Problem 82
Problem 83
Problem 84
Problem 85
Problem 86
Problem 87
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

Okay, let's find the derivative of capital f of tea. We have e to the power T sign of two T. And in general, the derivative of E to a function is each of the function times the derivative of the function. So this would be e to the t sign of two t times the derivative of tea. Sign of two t and t sign of two t is a product. So we need to use the product rule to find the derivative. So it would be the first tee times the derivative of the second, the derivative of Sinus co sign. So we have co sign to tee times the derivative of the inside the derivative of two tea is too. So that was chain rule right there. So we have the first times the derivative of the second plus the second sign of two t times. The derivative of the first derivative of tea is one. Okay, so we can write this as e to the T sign of two t times. Now will simplify this term here, and we'll call it to t co sign to t plus sign of two t

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Calculus: Early Transcendentals

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Related Topics

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Top Calculus 1 / AB Educators
Catherine Ross

Missouri State University

Heather Zimmers

Oregon State University

Caleb Elmore

Baylor University

Joseph Lentino

Boston College

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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