Problem

Find the derivative of the function. $ y = e^{\s…

01:47

Problem 39 Hard Difficulty

Find the derivative of the function.
$ f(t) = \tan (\sec(\cos t)) $

Answer

$=-\sec ^{2}(\sec (\cos t)) \sec (\cos t) \tan (\cos t) \sin t$

More Answers

00:42

Frank L.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Discussion

You must be signed in to discuss.

Top Calculus 1 / AB Educators

Grace H.

Kayleah T.

Harvey Mudd College

Michael J.

Idaho State University

Joseph L.

Boston College

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

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

we're going to use the chain rule to find the derivative of this function. And here we have an inside layer co sign a middle layer, see camp and an outside lawyer tangent. So there's three derivatives who are multiplying together. So we start with the outermost layer tangent, and it's derivative is he can't squared. So we have c can't squared of C can't of co sign t. Now we move on to the second layer. See can't. And the derivative of C camp is C camp times tangent. So we have C can't of co sign t times tangent of co sign t. Then we move on to the inside layer, which is co sign and it's derivative is negative signs. We have negative sign of teeth now. There's really nothing that combines here. So the only thing we could do for simplifying is to take this negative sign and bring it out to the front. Kind of a shame to have to rewrite the whole thing just to do that. Um, but that's convention now. It doesn't matter what order we put each of these terms in, So if you look it up in the back of the book, and they have the terms in a different order. That's okay, because it's just a product, and we know that we could multiply things in a variety of orders. That's the community of property, of multiplication, and there we have our derivative.

Heather Z.

Oregon State University

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Top Calculus 1 / AB Educators

Grace H.

Numerade Educator

Kayleah T.

Harvey Mudd College

Michael J.

Idaho State University

Joseph L.

Boston College