Calculus of a Single Variable
Calculus of a Single Variable
11th Edition
ISBN: 9781337275361
Author: Ron Larson, Bruce H. Edwards
Publisher: Cengage Learning
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Chapter 2.4, Problem 109E

(a)

To determine

To Calculate: The first, second, third and fourth order derivatives of the function f(x)=sinβx.

(b)

To determine

To Prove: That the function and its second derivative satisfy the equation f″(x)+β2f(x)=0 where f(x)=sinβx, β is a constant.

(c)

To determine

General rules for the even and odd order derivatives f2k(x) and f2k−1(x) for the function f(x)=sinβx, where β is a constant.

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Chapter 2 Solutions

Calculus of a Single Variable

Ch. 2.1 - Tangent Line Describe how to find the slope of the...Ch. 2.1 - Notation List four notation alternatives to f(x).Ch. 2.1 - Prob. 3ECh. 2.1 - Continuity and Differentiability Describe the...Ch. 2.1 - Estimating Slope In Exercises 5 and 6, estimate...Ch. 2.1 - Estimating Slope In Exercises 5 and 6, estimate...Ch. 2.1 - Slopes of Secant Lines In Exercises 7 and 8, use...Ch. 2.1 - Slopes of Secant Lines In Exercises 7 and 8. use...Ch. 2.1 - Finding the Slope of a Tangent Line In Exercises...Ch. 2.1 - Prob. 10E
Ch. 2.1 - Finding the Slope of a Tangent Line In Exercises...Ch. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - Finding the Slope of a Tangent Line In Exercises...Ch. 2.1 - Prob. 15ECh. 2.1 - Prob. 16ECh. 2.1 - Finding the Derivative by the Limit Process In...Ch. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Finding the Derivative by the Limit Process In...Ch. 2.1 - Prob. 22ECh. 2.1 - Finding the Derivative by the Limit Process In...Ch. 2.1 - Prob. 24ECh. 2.1 - Finding the Derivative by the Limit Process In...Ch. 2.1 - Prob. 26ECh. 2.1 - Prob. 27ECh. 2.1 - Finding the Derivative by the Limit Process In...Ch. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.1 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.1 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.1 - Prob. 39ECh. 2.1 - Prob. 40ECh. 2.1 - Prob. 41ECh. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Prob. 45ECh. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.1 - Prob. 48ECh. 2.1 - Prob. 49ECh. 2.1 - Prob. 50ECh. 2.1 - Prob. 51ECh. 2.1 - Symmetry of a Graph A function f is symmetric with...Ch. 2.1 - Using a Tangent Line The tangent line to the graph...Ch. 2.1 - Prob. 54ECh. 2.1 - Working Backwards In Exercises 55-58, the Unlit...Ch. 2.1 - Working Backwards In Exercises 55-58, the Unlit...Ch. 2.1 - Prob. 57ECh. 2.1 - Prob. 58ECh. 2.1 - Writing a Function Using Derivatives In Exercises...Ch. 2.1 - Prob. 60ECh. 2.1 - Prob. 61ECh. 2.1 - Prob. 62ECh. 2.1 - Prob. 63ECh. 2.1 - HOW DO YOU SEE IT? The figure shows die graph of...Ch. 2.1 - Prob. 65ECh. 2.1 - Prob. 66ECh. 2.1 - Prob. 67ECh. 2.1 - Prob. 68ECh. 2.1 - Prob. 69ECh. 2.1 - Prob. 70ECh. 2.1 - Prob. 71ECh. 2.1 - Prob. 72ECh. 2.1 - Prob. 73ECh. 2.1 - Using the Alternative Form of the Derivative In...Ch. 2.1 - Prob. 75ECh. 2.1 - Prob. 76ECh. 2.1 - Prob. 77ECh. 2.1 - Prob. 78ECh. 2.1 - Prob. 79ECh. 2.1 - Determining Differentiability In Exercises 77-80,...Ch. 2.1 - Prob. 81ECh. 2.1 - Prob. 82ECh. 2.1 - Prob. 83ECh. 2.1 - Prob. 84ECh. 2.1 - Prob. 85ECh. 2.1 - Determining Differentiability In Exercises 85-88,...Ch. 2.1 - Determining Differentiability In Exercises 85-88,...Ch. 2.1 - Prob. 88ECh. 2.1 - Prob. 89ECh. 2.1 - Prob. 90ECh. 2.1 - Graphical Reasoning A line with slope m passes...Ch. 2.1 - Conjecture Consider the functions f(x)=x2 and...Ch. 2.1 - Prob. 93ECh. 2.1 - Prob. 94ECh. 2.1 - Prob. 95ECh. 2.1 - Prob. 96ECh. 2.1 - Prob. 97ECh. 2.1 - Writing Use a graphing utility to graph the two...Ch. 2.2 - CONCEPT CHECK Constant Rule What is the derivative...Ch. 2.2 - Prob. 2ECh. 2.2 - Derivatives of Trigonometric Functions What are...Ch. 2.2 - Prob. 4ECh. 2.2 - Prob. 5ECh. 2.2 - Estimating Slope In Exercises 5 and 6, use the...Ch. 2.2 - Finding a Derivative In Exercises 7-26. Use the...Ch. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Prob. 10ECh. 2.2 - Prob. 11ECh. 2.2 - Prob. 12ECh. 2.2 - Prob. 13ECh. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Finding a Derivative In Exercises 7-26. use the...Ch. 2.2 - Prob. 18ECh. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Rewriting a Function Before Differentiating In...Ch. 2.2 - Rewriting a Function Before Differentiating In...Ch. 2.2 - Rewriting a Function Before Differentiating In...Ch. 2.2 - Rewriting a Function Before Differentiating In...Ch. 2.2 - Finding the Slope of a Graph In Exercises 31-38,...Ch. 2.2 - Prob. 32ECh. 2.2 - Prob. 33ECh. 2.2 - Prob. 34ECh. 2.2 - Prob. 35ECh. 2.2 - Prob. 36ECh. 2.2 - Prob. 37ECh. 2.2 - Finding the Slope of a Graph In Exercises 31-38,...Ch. 2.2 - Finding a Derivative In Exercises 39-54, find the...Ch. 2.2 - Prob. 40ECh. 2.2 - Prob. 41ECh. 2.2 - Prob. 42ECh. 2.2 - Prob. 43ECh. 2.2 - Prob. 44ECh. 2.2 - Finding a Derivative In Exercises 39-54, find the...Ch. 2.2 - Finding a Derivative In Exercises 39-54, find the...Ch. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - Prob. 49ECh. 2.2 - Prob. 50ECh. 2.2 - Prob. 51ECh. 2.2 - Finding a Derivative In Exercises 39-54, find the...Ch. 2.2 - Prob. 53ECh. 2.2 - Prob. 54ECh. 2.2 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.2 - Prob. 56ECh. 2.2 - Prob. 57ECh. 2.2 - Prob. 58ECh. 2.2 - Horizontal Tangent Line In Exercises 59-64....Ch. 2.2 - Horizontal Tangent Line In Exercises 59-64....Ch. 2.2 - Prob. 61ECh. 2.2 - Prob. 62ECh. 2.2 - Prob. 63ECh. 2.2 - Horizontal Tangent Line In Exercises 59-64....Ch. 2.2 - Prob. 65ECh. 2.2 - Finding a Value In Exercises 65-68, find k such...Ch. 2.2 - Finding a Value In Exercises 65-68, find k such...Ch. 2.2 - Prob. 68ECh. 2.2 - Prob. 69ECh. 2.2 - Prob. 70ECh. 2.2 - Prob. 71ECh. 2.2 - Prob. 72ECh. 2.2 - Prob. 73ECh. 2.2 - Prob. 74ECh. 2.2 - Prob. 75ECh. 2.2 - Prob. 76ECh. 2.2 - Prob. 77ECh. 2.2 - Tangent Lines Show that the graphs of the two...Ch. 2.2 - Horizontal Tangent Line Show that the graph of the...Ch. 2.2 - Prob. 80ECh. 2.2 - Prob. 81ECh. 2.2 - Prob. 82ECh. 2.2 - Prob. 83ECh. 2.2 - Prob. 84ECh. 2.2 - Prob. 85ECh. 2.2 - Prob. 86ECh. 2.2 - Prob. 87ECh. 2.2 - Prob. 88ECh. 2.2 - Prob. 89ECh. 2.2 - Prob. 90ECh. 2.2 - Prob. 91ECh. 2.2 - Prob. 92ECh. 2.2 - Prob. 93ECh. 2.2 - Prob. 94ECh. 2.2 - Prob. 95ECh. 2.2 - Vertical Motion In Exercises 95 and 96, use the...Ch. 2.2 - Prob. 97ECh. 2.2 - Vertical Motion In Exercises 97 and 98, use the...Ch. 2.2 - Prob. 99ECh. 2.2 - Prob. 100ECh. 2.2 - Prob. 101ECh. 2.2 - Prob. 102ECh. 2.2 - Modeling Data The stopping distance of an...Ch. 2.2 - Fuel Cost A car is driven 15,000 miles a year and...Ch. 2.2 - Prob. 105ECh. 2.2 - Inventory Management The annual inventory cost C...Ch. 2.2 - Prob. 107ECh. 2.2 - Proof Lei (a, b) be an arbitrary point on the...Ch. 2.2 - Prob. 109ECh. 2.2 - Prob. 110ECh. 2.2 - Prob. 111ECh. 2.2 - Prob. 112ECh. 2.2 - Prob. 113ECh. 2.2 - Prob. 114ECh. 2.2 - Find all differentiable functions f: such that...Ch. 2.3 - CONCEPT CHECK Product Rule Describe the Product...Ch. 2.3 - Prob. 2ECh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Using the Product Rule In Exercises 5-10. use the...Ch. 2.3 - Using the Product Rule In Exercises 5-10. use the...Ch. 2.3 - Using the Product Rule In Exercises 5-10. use the...Ch. 2.3 - Using the Product Rule In Exercises 5-10. use the...Ch. 2.3 - Using the Product Rule In Exercises 5-10. use the...Ch. 2.3 - Using the Product Rule In Exercises 5-10. use the...Ch. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 2.3 - Prob. 13ECh. 2.3 - Prob. 14ECh. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Finding and Evaluating a Derivative In Exercises...Ch. 2.3 - Prob. 18ECh. 2.3 - Finding and Evaluating a Derivative In Exercises...Ch. 2.3 - Finding and Evaluating a Derivative In Exercises...Ch. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Prob. 28ECh. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - Finding a Derivative In Exercises 29-40, Find the...Ch. 2.3 - Prob. 35ECh. 2.3 - Prob. 36ECh. 2.3 - Prob. 37ECh. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.3 - Prob. 40ECh. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.3 - Finding a Derivative of a Trigonometric Function...Ch. 2.3 - Prob. 48ECh. 2.3 - Finding a Derivative of a Trigonometric Function...Ch. 2.3 - Prob. 50ECh. 2.3 - Prob. 51ECh. 2.3 - Prob. 52ECh. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.3 - Prob. 55ECh. 2.3 - Prob. 56ECh. 2.3 - Prob. 57ECh. 2.3 - Prob. 58ECh. 2.3 - Prob. 59ECh. 2.3 - Finding the Slope of a Graph In Exercises 59-62,...Ch. 2.3 - Finding the Slope of a Graph In Exercises 59-62,...Ch. 2.3 - Prob. 62ECh. 2.3 - Prob. 63ECh. 2.3 - Prob. 64ECh. 2.3 - Prob. 65ECh. 2.3 - Prob. 66ECh. 2.3 - Prob. 67ECh. 2.3 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.3 - Prob. 69ECh. 2.3 - Prob. 70ECh. 2.3 - Prob. 71ECh. 2.3 - Famous Curves In Exercises 69-72, find an equation...Ch. 2.3 - Prob. 73ECh. 2.3 - Prob. 74ECh. 2.3 - Prob. 75ECh. 2.3 - Horizontal Tangent Line In Exercises 73-76....Ch. 2.3 - Prob. 77ECh. 2.3 - Prob. 78ECh. 2.3 - Prob. 79ECh. 2.3 - Prob. 80ECh. 2.3 - Prob. 81ECh. 2.3 - Finding Derivatives In Exercises 81 and 82, use...Ch. 2.3 - Prob. 83ECh. 2.3 - Prob. 84ECh. 2.3 - Prob. 85ECh. 2.3 - Prob. 86ECh. 2.3 - Prob. 87ECh. 2.3 - Rate of Change Determine whether there exist any...Ch. 2.3 - Prob. 89ECh. 2.3 - Prob. 90ECh. 2.3 - Prob. 91ECh. 2.3 - Prob. 92ECh. 2.3 - Prob. 93ECh. 2.3 - Prob. 94ECh. 2.3 - Prob. 95ECh. 2.3 - Prob. 96ECh. 2.3 - Prob. 97ECh. 2.3 - Prob. 98ECh. 2.3 - Prob. 99ECh. 2.3 - Prob. 100ECh. 2.3 - Prob. 101ECh. 2.3 - Prob. 102ECh. 2.3 - Prob. 103ECh. 2.3 - Prob. 104ECh. 2.3 - Prob. 105ECh. 2.3 - Prob. 106ECh. 2.3 - Prob. 107ECh. 2.3 - Prob. 108ECh. 2.3 - Higher-Order Derivatives Polynomials of what...Ch. 2.3 - Prob. 110ECh. 2.3 - Prob. 111ECh. 2.3 - Prob. 112ECh. 2.3 - Prob. 113ECh. 2.3 - Prob. 114ECh. 2.3 - Prob. 115ECh. 2.3 - Prob. 116ECh. 2.3 - Prob. 117ECh. 2.3 - Prob. 118ECh. 2.3 - Prob. 119ECh. 2.3 - Prob. 120ECh. 2.3 - Prob. 121ECh. 2.3 - Prob. 122ECh. 2.3 - Finding a Pattern Consider the function...Ch. 2.3 - Prob. 124ECh. 2.3 - Prob. 125ECh. 2.3 - Prob. 126ECh. 2.3 - Prob. 127ECh. 2.3 - Prob. 128ECh. 2.3 - Prob. 129ECh. 2.3 - Prob. 130ECh. 2.3 - Prob. 131ECh. 2.3 - Prob. 132ECh. 2.3 - Prob. 133ECh. 2.3 - Prob. 134ECh. 2.3 - Prob. 135ECh. 2.3 - Prob. 136ECh. 2.3 - Prob. 137ECh. 2.3 - Prob. 138ECh. 2.4 - Chain Rule Describe the Chain Rule for the...Ch. 2.4 - General Power Rule What is the difference between...Ch. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - Prob. 6ECh. 2.4 - Prob. 7ECh. 2.4 - Prob. 8ECh. 2.4 - Prob. 9ECh. 2.4 - Prob. 10ECh. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - Finding a Derivative In Exercises 9-34, find the...Ch. 2.4 - Prob. 15ECh. 2.4 - Finding a Derivative In Exercises 9-34, find the...Ch. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - Prob. 22ECh. 2.4 - Finding a Derivative In Exercises 9-34, find the...Ch. 2.4 - Prob. 24ECh. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Prob. 28ECh. 2.4 - Prob. 29ECh. 2.4 - Prob. 30ECh. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Finding a Derivative of a Trigonometric Function...Ch. 2.4 - Prob. 40ECh. 2.4 - Prob. 41ECh. 2.4 - Finding a Derivative of a Trigonometric Function...Ch. 2.4 - Prob. 43ECh. 2.4 - Prob. 44ECh. 2.4 - Prob. 45ECh. 2.4 - Prob. 46ECh. 2.4 - Finding a Derivative of a Trigonometric Function...Ch. 2.4 - Prob. 48ECh. 2.4 - Finding a Derivative of a Trigonometric Function...Ch. 2.4 - Prob. 50ECh. 2.4 - Finding a Derivative of a Trigonometric Function...Ch. 2.4 - Prob. 52ECh. 2.4 - Prob. 53ECh. 2.4 - Prob. 54ECh. 2.4 - Prob. 55ECh. 2.4 - Prob. 56ECh. 2.4 - Prob. 57ECh. 2.4 - Prob. 58ECh. 2.4 - Prob. 59ECh. 2.4 - Prob. 60ECh. 2.4 - Prob. 61ECh. 2.4 - Prob. 62ECh. 2.4 - Prob. 63ECh. 2.4 - Prob. 64ECh. 2.4 - Prob. 65ECh. 2.4 - Prob. 66ECh. 2.4 - Prob. 67ECh. 2.4 - Prob. 68ECh. 2.4 - Prob. 69ECh. 2.4 - Prob. 70ECh. 2.4 - Prob. 71ECh. 2.4 - Prob. 72ECh. 2.4 - Prob. 73ECh. 2.4 - Prob. 74ECh. 2.4 - Prob. 75ECh. 2.4 - Prob. 76ECh. 2.4 - Prob. 77ECh. 2.4 - Prob. 78ECh. 2.4 - Prob. 79ECh. 2.4 - Famous Curves In Exercises 79 and 80, find an...Ch. 2.4 - Prob. 81ECh. 2.4 - Prob. 82ECh. 2.4 - Prob. 83ECh. 2.4 - Prob. 84ECh. 2.4 - Prob. 85ECh. 2.4 - Prob. 86ECh. 2.4 - Prob. 87ECh. 2.4 - Prob. 88ECh. 2.4 - Prob. 89ECh. 2.4 - Prob. 90ECh. 2.4 - Prob. 91ECh. 2.4 - Prob. 92ECh. 2.4 - Prob. 93ECh. 2.4 - Prob. 94ECh. 2.4 - Prob. 95ECh. 2.4 - Prob. 96ECh. 2.4 - Think about It The table shows some values of the...Ch. 2.4 - Prob. 98ECh. 2.4 - Prob. 99ECh. 2.4 - Prob. 100ECh. 2.4 - Prob. 101ECh. 2.4 - Prob. 102ECh. 2.4 - Pendulum A 15-centimeter pendulum moves according...Ch. 2.4 - Prob. 104ECh. 2.4 - Prob. 105ECh. 2.4 - Prob. 106ECh. 2.4 - Prob. 107ECh. 2.4 - Depreciation The value V of a machine t years...Ch. 2.4 - Prob. 109ECh. 2.4 - Prob. 110ECh. 2.4 - Think About It Let r(x)=f(g(x)) and s(x)=g(f(x)),...Ch. 2.4 - Prob. 112ECh. 2.4 - Prob. 113ECh. 2.4 - Prob. 114ECh. 2.4 - Prob. 115ECh. 2.4 - Prob. 116ECh. 2.4 - Prob. 117ECh. 2.4 - Prob. 118ECh. 2.4 - Prob. 119ECh. 2.4 - Prob. 120ECh. 2.4 - Prob. 121ECh. 2.4 - Prob. 122ECh. 2.4 - Prob. 123ECh. 2.4 - Prob. 124ECh. 2.4 - PUTNAM EXAM CHALLENGE Let...Ch. 2.4 - Prob. 126ECh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Finding a Derivative In Exercises 5-20, find dy /...Ch. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - Finding a Derivative In Exercises 5-20, find dy /...Ch. 2.5 - Prob. 11ECh. 2.5 - Finding a Derivative In Exercises 5-20, find dy /...Ch. 2.5 - Prob. 13ECh. 2.5 - Finding a Derivative In Exercises 5-20, find dy /...Ch. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - Finding a Derivative In Exercises 5-20, find dy /...Ch. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.5 - Prob. 29ECh. 2.5 - Prob. 30ECh. 2.5 - Prob. 31ECh. 2.5 - Prob. 32ECh. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - Famous Curves In Exercises 39-42, find the slope...Ch. 2.5 - Prob. 36ECh. 2.5 - Prob. 37ECh. 2.5 - Prob. 38ECh. 2.5 - Prob. 39ECh. 2.5 - Prob. 40ECh. 2.5 - Prob. 41ECh. 2.5 - Prob. 42ECh. 2.5 - Prob. 43ECh. 2.5 - Prob. 44ECh. 2.5 - Prob. 45ECh. 2.5 - Prob. 46ECh. 2.5 - Prob. 47ECh. 2.5 - Prob. 48ECh. 2.5 - Finding a Second Derivative In Exercises 49-54....Ch. 2.5 - Prob. 50ECh. 2.5 - Finding a Second Derivative In Exercises 49-54,...Ch. 2.5 - Prob. 52ECh. 2.5 - Finding a Second Derivative In Exercises, 49-54....Ch. 2.5 - Prob. 54ECh. 2.5 - Prob. 55ECh. 2.5 - Prob. 56ECh. 2.5 - Prob. 57ECh. 2.5 - Prob. 58ECh. 2.5 - Prob. 59ECh. 2.5 - Prob. 60ECh. 2.5 - Vertical and Horizontal Tangent Lines In Exercises...Ch. 2.5 - Prob. 62ECh. 2.5 - Prob. 63ECh. 2.5 - Prob. 64ECh. 2.5 - Prob. 65ECh. 2.5 - Prob. 66ECh. 2.5 - Prob. 67ECh. 2.5 - Prob. 68ECh. 2.5 - Orthogonal Trajectories The figure below shows the...Ch. 2.5 - Prob. 70ECh. 2.5 - Prob. 71ECh. 2.5 - Tangent Lines and Intercepts Let l. be any tangent...Ch. 2.5 - Proof (a) Prove (Theorem 3.3) that d/dxxn=nxn1 for...Ch. 2.5 - Slope Find all points on the circle x2+y2=100...Ch. 2.5 - Prob. 75ECh. 2.5 - Prob. 76ECh. 2.5 - Normal Lines (a) Find an equation of the normal...Ch. 2.6 - Related-Rate Equation What is a related-rate...Ch. 2.6 - Prob. 2ECh. 2.6 - Using Related Rates In Exercises 3-6, assume that...Ch. 2.6 - Using Related Rates In Exercises 3-6, assume that...Ch. 2.6 - Using Related Rates In Exercises 3-6, assume that...Ch. 2.6 - Using Related Rates In Exercises 3-6, assume that...Ch. 2.6 - Moving Point In Exercises 7-10, a point is moving...Ch. 2.6 - Prob. 8ECh. 2.6 - Prob. 9ECh. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - Area The length .v of each side of an equilateral...Ch. 2.6 - Volume The radius r of a sphere is increasing at a...Ch. 2.6 - Radius A spherical balloon is inflated with gas at...Ch. 2.6 - Prob. 15ECh. 2.6 - Prob. 16ECh. 2.6 - Prob. 17ECh. 2.6 - Height The volume of oil in a cylindrical...Ch. 2.6 - Depth A swimming pool is 12 meters long, 6 meters...Ch. 2.6 - Depth A trough is 12 feet long and 3 feet across...Ch. 2.6 - Moving Ladder A ladder 25 feet long is leaning...Ch. 2.6 - Prob. 22ECh. 2.6 - Construction A winch at the top of a 12-meter...Ch. 2.6 - Boating A boat is pulled into a dock by means of a...Ch. 2.6 - Air Traffic Control An air traffic controller...Ch. 2.6 - Air Traffic Control An airplane is flying at an...Ch. 2.6 - Prob. 27ECh. 2.6 - Sports For (be baseball diamond in Exercise 27,...Ch. 2.6 - Shadow Length A man 6 feet tall walks at a rate of...Ch. 2.6 - Prob. 30ECh. 2.6 - Machine Design The endpoints of a movable rod of...Ch. 2.6 - Machine Design Repeat Exercise 31 for a position...Ch. 2.6 - Prob. 33ECh. 2.6 - Prob. 34ECh. 2.6 - Prob. 35ECh. 2.6 - Prob. 36ECh. 2.6 - Prob. 37ECh. 2.6 - Prob. 38ECh. 2.6 - Flight Control An airplane is flying in still air...Ch. 2.6 - Angle of Elevation A balloon rises at a rate of 4...Ch. 2.6 - Angle of Elevation A fish is reeled in at a rate...Ch. 2.6 - Angle of Elevation An airplane flies at an...Ch. 2.6 - Linear vs. Angular Speed A patrol car is parked 50...Ch. 2.6 - Linear vs. Angular Speed A wheel of radius 30...Ch. 2.6 - Prob. 45ECh. 2.6 - Security Camera A security camera is centered 50...Ch. 2.6 - Prob. 47ECh. 2.6 - Moving Shadow A ball is dropped from a height of...Ch. 2.6 - Prob. 49ECh. 2.6 - Acceleration In Exercises 49 and 50, find the...Ch. 2 - Finding the Derivative by the Limit Process In...Ch. 2 - Finding the Derivative by the Limit Process In...Ch. 2 - Finding the Derivative by the Limit Process In...Ch. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Determining Differentiability In Exercises 7 and...Ch. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Finding a Derivative In Exercises 9-20, use the...Ch. 2 - Prob. 12RECh. 2 - Finding a Derivative In Exercises 9-20, use (he...Ch. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - Prob. 23RECh. 2 - Prob. 24RECh. 2 - Prob. 25RECh. 2 - Prob. 26RECh. 2 - Prob. 27RECh. 2 - Vertical Motion In Exercises 27 and 28, use the...Ch. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - Prob. 31RECh. 2 - Prob. 32RECh. 2 - Finding a Derivative In Exercises 29-40, use the...Ch. 2 - Finding a Derivative In Exercises 29-40, use the...Ch. 2 - Finding a Derivative In Exercises 29-40, use the...Ch. 2 - Prob. 36RECh. 2 - Prob. 37RECh. 2 - Prob. 38RECh. 2 - Prob. 39RECh. 2 - Prob. 40RECh. 2 - Prob. 41RECh. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - Finding a Second Derivative In Exercises 4552,...Ch. 2 - Prob. 50RECh. 2 - Prob. 51RECh. 2 - Prob. 52RECh. 2 - Prob. 53RECh. 2 - Prob. 54RECh. 2 - Prob. 55RECh. 2 - Prob. 56RECh. 2 - Prob. 57RECh. 2 - Prob. 58RECh. 2 - Prob. 59RECh. 2 - Prob. 60RECh. 2 - Prob. 61RECh. 2 - Prob. 62RECh. 2 - Prob. 63RECh. 2 - Prob. 64RECh. 2 - Prob. 65RECh. 2 - Prob. 66RECh. 2 - Prob. 67RECh. 2 - Prob. 68RECh. 2 - Prob. 69RECh. 2 - Prob. 70RECh. 2 - Prob. 71RECh. 2 - Prob. 72RECh. 2 - Prob. 73RECh. 2 - Prob. 74RECh. 2 - Prob. 75RECh. 2 - Prob. 76RECh. 2 - Refrigeration The temperature T (in degrees...Ch. 2 - Prob. 78RECh. 2 - Prob. 79RECh. 2 - Prob. 80RECh. 2 - Prob. 81RECh. 2 - Prob. 82RECh. 2 - Prob. 83RECh. 2 - Prob. 84RECh. 2 - Prob. 85RECh. 2 - Prob. 86RECh. 2 - Prob. 87RECh. 2 - Prob. 88RECh. 2 - Linear vs. Angular Speed A routing beacon is...Ch. 2 - Moving Shadow A sandbag is dropped from a balloon...Ch. 2 - Prob. 1PSCh. 2 - Prob. 2PSCh. 2 - Prob. 3PSCh. 2 - Prob. 4PSCh. 2 - Prob. 5PSCh. 2 - Prob. 6PSCh. 2 - Prob. 7PSCh. 2 - Famous Curve The graph of the pear-shaped quartic...Ch. 2 - Shadow Length A man 6 feet tall walks at a rate of...Ch. 2 - Moving Point A particle is moving along the graph...Ch. 2 - Projectile Motion An astronaut standing on the...Ch. 2 - Prob. 12PSCh. 2 - Prob. 13PSCh. 2 - Prob. 14PSCh. 2 - Acceleration and Jerk If a is the acceleration of...
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Chain Rule dy:dx = dy:du*du:dx; Author: Robert Cappetta;https://www.youtube.com/watch?v=IUYniALwbHs;License: Standard YouTube License, CC-BY
CHAIN RULE Part 1; Author: Btech Maths Hub;https://www.youtube.com/watch?v=TIAw6AJ_5Po;License: Standard YouTube License, CC-BY