Calculus
5th Edition
ISBN: 9781429241861
Author: Laura Taalman, Peter Kohn
Publisher: W. H. Freeman
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Question
Chapter 2.5, Problem 48S
To determine
To find: The derivative of the given function.
Expert Solution & Answer
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Check out a sample textbook solutionStudents have asked these similar questions
In Exercises 3–10, differentiate the expression with respect to x, assuming
that y is implicitly a function of x.
Each of Exercises 81–84 shows the graphs of the first and second
derivatives of a function y = f(x). Copy the picture and add to it a
sketch of the approximate graph of f, given that the graph passes
through the point P.
Suppose f and g are the piecewise-defined functions defined
here. For each combination of functions in Exercises 51–56,
(a) find its values at x = -1, x = 0, x = 1, x = 2, and x = 3,
(b) sketch its graph, and (c) write the combination as a
piecewise-defined function.
f(x) = {
(2x + 1, ifx 0
g(x) = {
-x, if x 2
8(4):
51. (f+g)(x)
52. 3f(x)
53. (gof)(x)
56. g(3x)
54. f(x) – 1
55. f(x – 1)
Chapter 2 Solutions
Calculus
Ch. 2.1 - Prob. 1TBCh. 2.1 - Prob. 2TBCh. 2.1 - Prob. 3TBCh. 2.1 - Prob. 4TBCh. 2.1 - Prob. 0CCh. 2.1 - Prob. 1CCh. 2.1 - Prob. 2CCh. 2.1 - Prob. 3CCh. 2.1 - Prob. 4CCh. 2.1 - Prob. 5C
Ch. 2.1 - Prob. 6CCh. 2.1 - Prob. 7CCh. 2.1 - Prob. 8CCh. 2.1 - Prob. 9CCh. 2.1 - Prob. 10CCh. 2.1 - Prob. 11CCh. 2.1 - Prob. 12CCh. 2.1 - Prob. 13CCh. 2.1 - Prob. 14CCh. 2.1 - Prob. 15CCh. 2.1 - Prob. 16CCh. 2.1 - Prob. 17CCh. 2.1 - Prob. 18CCh. 2.1 - Prob. 19CCh. 2.1 - Prob. 20CCh. 2.1 - Prob. 21SCh. 2.1 - Prob. 22SCh. 2.1 - Prob. 23SCh. 2.1 - Prob. 24SCh. 2.1 - Prob. 25SCh. 2.1 - Prob. 26SCh. 2.1 - Prob. 27SCh. 2.1 - Prob. 28SCh. 2.1 - Prob. 29SCh. 2.1 - Prob. 30SCh. 2.1 - Prob. 31SCh. 2.1 - Prob. 32SCh. 2.1 - Prob. 33SCh. 2.1 - Prob. 34SCh. 2.1 - Prob. 35SCh. 2.1 - Prob. 36SCh. 2.1 - Prob. 37SCh. 2.1 - Prob. 38SCh. 2.1 - Prob. 39SCh. 2.1 - Prob. 40SCh. 2.1 - Prob. 41SCh. 2.1 - Prob. 42SCh. 2.1 - Prob. 43SCh. 2.1 - Prob. 44SCh. 2.1 - Prob. 45ACh. 2.1 - Prob. 46ACh. 2.1 - Prob. 47ACh. 2.1 - Prob. 48ACh. 2.1 - Prob. 49ACh. 2.1 - Prob. 50ACh. 2.1 - Prob. 51ACh. 2.1 - Prob. 52ACh. 2.1 - Prob. 53ACh. 2.1 - Prob. 54ACh. 2.1 - Prob. 55ACh. 2.1 - Prob. 56ACh. 2.1 - Prob. 57ACh. 2.1 - Prob. 58PCh. 2.1 - Prob. 59PCh. 2.1 - Prob. 1TFCh. 2.1 - Prob. 2TFCh. 2.1 - Prob. 3TFCh. 2.2 - Prob. 1TBCh. 2.2 - Prob. 2TBCh. 2.2 - Prob. 0CCh. 2.2 - Prob. 1CCh. 2.2 - Prob. 2CCh. 2.2 - Prob. 3CCh. 2.2 - Prob. 4CCh. 2.2 - Prob. 5CCh. 2.2 - Prob. 6CCh. 2.2 - Prob. 7CCh. 2.2 - Prob. 8CCh. 2.2 - Prob. 9CCh. 2.2 - Prob. 10CCh. 2.2 - Prob. 11CCh. 2.2 - Prob. 12CCh. 2.2 - Prob. 13CCh. 2.2 - Prob. 14CCh. 2.2 - Prob. 15CCh. 2.2 - Prob. 16CCh. 2.2 - Prob. 17CCh. 2.2 - Prob. 18CCh. 2.2 - Prob. 19CCh. 2.2 - Prob. 20CCh. 2.2 - Prob. 21CCh. 2.2 - Prob. 22CCh. 2.2 - Prob. 23SCh. 2.2 - Prob. 24SCh. 2.2 - Prob. 25SCh. 2.2 - Prob. 26SCh. 2.2 - Prob. 27SCh. 2.2 - Prob. 28SCh. 2.2 - Prob. 29SCh. 2.2 - Prob. 30SCh. 2.2 - Prob. 31SCh. 2.2 - Prob. 32SCh. 2.2 - Prob. 33SCh. 2.2 - Prob. 34SCh. 2.2 - Prob. 35SCh. 2.2 - Prob. 36SCh. 2.2 - Prob. 37SCh. 2.2 - Prob. 38SCh. 2.2 - Prob. 39SCh. 2.2 - Prob. 40SCh. 2.2 - Prob. 41SCh. 2.2 - Prob. 42SCh. 2.2 - Prob. 43SCh. 2.2 - Prob. 44SCh. 2.2 - Prob. 45SCh. 2.2 - Prob. 46SCh. 2.2 - Prob. 47SCh. 2.2 - Prob. 48SCh. 2.2 - Prob. 49SCh. 2.2 - Prob. 50SCh. 2.2 - Prob. 51SCh. 2.2 - Prob. 52SCh. 2.2 - Prob. 53SCh. 2.2 - Prob. 54SCh. 2.2 - Prob. 55SCh. 2.2 - Prob. 56SCh. 2.2 - Prob. 57SCh. 2.2 - Prob. 58SCh. 2.2 - Prob. 59SCh. 2.2 - Prob. 60SCh. 2.2 - Prob. 61SCh. 2.2 - Prob. 62SCh. 2.2 - Prob. 63SCh. 2.2 - Prob. 64SCh. 2.2 - Prob. 65SCh. 2.2 - Prob. 66SCh. 2.2 - Prob. 67SCh. 2.2 - Prob. 68SCh. 2.2 - Prob. 69SCh. 2.2 - Prob. 70SCh. 2.2 - Prob. 71SCh. 2.2 - Prob. 72SCh. 2.2 - Prob. 73SCh. 2.2 - Prob. 74SCh. 2.2 - Prob. 75SCh. 2.2 - Prob. 76SCh. 2.2 - Prob. 77SCh. 2.2 - Prob. 78SCh. 2.2 - Prob. 79SCh. 2.2 - Prob. 80SCh. 2.2 - Prob. 81SCh. 2.2 - Prob. 82SCh. 2.2 - Prob. 83SCh. 2.2 - Prob. 84SCh. 2.2 - Prob. 85SCh. 2.2 - Prob. 86SCh. 2.2 - Prob. 87ACh. 2.2 - Prob. 88ACh. 2.2 - Prob. 89ACh. 2.2 - Prob. 90ACh. 2.2 - Prob. 91ACh. 2.2 - Prob. 92PCh. 2.2 - Prob. 93PCh. 2.2 - Prob. 94PCh. 2.2 - Prob. 95PCh. 2.2 - Prob. 96PCh. 2.2 - Prob. 97PCh. 2.2 - Prob. 98PCh. 2.2 - Prob. 1TFCh. 2.2 - Prob. 2TFCh. 2.2 - 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Prob. 48SCh. 2.3 - Prob. 49SCh. 2.3 - Prob. 50SCh. 2.3 - Prob. 51SCh. 2.3 - Prob. 52SCh. 2.3 - Prob. 53SCh. 2.3 - Prob. 54SCh. 2.3 - Prob. 55SCh. 2.3 - Prob. 56SCh. 2.3 - Prob. 57SCh. 2.3 - Prob. 58SCh. 2.3 - Prob. 59SCh. 2.3 - Prob. 60SCh. 2.3 - Prob. 61SCh. 2.3 - Prob. 62SCh. 2.3 - Prob. 63SCh. 2.3 - Prob. 64SCh. 2.3 - Prob. 65SCh. 2.3 - Prob. 66SCh. 2.3 - Prob. 67SCh. 2.3 - Prob. 68SCh. 2.3 - Prob. 69SCh. 2.3 - Prob. 70SCh. 2.3 - Prob. 71SCh. 2.3 - Prob. 72SCh. 2.3 - Prob. 73SCh. 2.3 - Prob. 74SCh. 2.3 - Prob. 75SCh. 2.3 - Prob. 76SCh. 2.3 - Prob. 77SCh. 2.3 - Prob. 78SCh. 2.3 - Prob. 79ACh. 2.3 - Prob. 80ACh. 2.3 - Prob. 81ACh. 2.3 - Prob. 82ACh. 2.3 - Prob. 83ACh. 2.3 - Prob. 84PCh. 2.3 - Prob. 85PCh. 2.3 - Prob. 86PCh. 2.3 - Prob. 87PCh. 2.3 - Prob. 88PCh. 2.3 - Prob. 89PCh. 2.3 - Prob. 90PCh. 2.3 - Prob. 91PCh. 2.3 - Prob. 92PCh. 2.3 - Prob. 1TFCh. 2.3 - Prob. 2TFCh. 2.3 - Prob. 3TFCh. 2.3 - Prob. 4TFCh. 2.3 - Prob. 5TFCh. 2.4 - Prob. 1TBCh. 2.4 - Prob. 2TBCh. 2.4 - Prob. 0CCh. 2.4 - Prob. 1CCh. 2.4 - Prob. 2CCh. 2.4 - Prob. 3CCh. 2.4 - Prob. 4CCh. 2.4 - Prob. 5CCh. 2.4 - Prob. 6CCh. 2.4 - Prob. 7CCh. 2.4 - Prob. 8CCh. 2.4 - Prob. 9CCh. 2.4 - Prob. 10CCh. 2.4 - Prob. 11CCh. 2.4 - Prob. 12CCh. 2.4 - Prob. 13CCh. 2.4 - Prob. 14CCh. 2.4 - Prob. 15CCh. 2.4 - Prob. 16CCh. 2.4 - Prob. 17CCh. 2.4 - Prob. 18CCh. 2.4 - Prob. 19CCh. 2.4 - Prob. 20CCh. 2.4 - Prob. 21SCh. 2.4 - Prob. 22SCh. 2.4 - Prob. 23SCh. 2.4 - Prob. 24SCh. 2.4 - Prob. 25SCh. 2.4 - Prob. 26SCh. 2.4 - Prob. 27SCh. 2.4 - Prob. 28SCh. 2.4 - Prob. 29SCh. 2.4 - Prob. 30SCh. 2.4 - Prob. 31SCh. 2.4 - Prob. 32SCh. 2.4 - Prob. 33SCh. 2.4 - Prob. 34SCh. 2.4 - Prob. 35SCh. 2.4 - Prob. 36SCh. 2.4 - Prob. 37SCh. 2.4 - Prob. 38SCh. 2.4 - Prob. 39SCh. 2.4 - Prob. 40SCh. 2.4 - Prob. 41SCh. 2.4 - Prob. 42SCh. 2.4 - Prob. 43SCh. 2.4 - Prob. 44SCh. 2.4 - Prob. 45SCh. 2.4 - Prob. 46SCh. 2.4 - Prob. 47SCh. 2.4 - Prob. 48SCh. 2.4 - Prob. 49SCh. 2.4 - Prob. 50SCh. 2.4 - Prob. 51SCh. 2.4 - Prob. 52SCh. 2.4 - Prob. 53SCh. 2.4 - Prob. 54SCh. 2.4 - Prob. 55SCh. 2.4 - Prob. 56SCh. 2.4 - Prob. 57SCh. 2.4 - Prob. 58SCh. 2.4 - Prob. 59SCh. 2.4 - Prob. 60SCh. 2.4 - Prob. 61SCh. 2.4 - Prob. 62SCh. 2.4 - Prob. 63SCh. 2.4 - Prob. 64SCh. 2.4 - Prob. 65SCh. 2.4 - Prob. 66SCh. 2.4 - Prob. 67SCh. 2.4 - Prob. 68SCh. 2.4 - Prob. 69SCh. 2.4 - Prob. 70SCh. 2.4 - Prob. 71SCh. 2.4 - Prob. 72SCh. 2.4 - Prob. 73SCh. 2.4 - Prob. 74SCh. 2.4 - Prob. 75SCh. 2.4 - Prob. 76SCh. 2.4 - Prob. 77SCh. 2.4 - Prob. 78SCh. 2.4 - Prob. 79SCh. 2.4 - Prob. 80SCh. 2.4 - Prob. 81SCh. 2.4 - Prob. 82SCh. 2.4 - Prob. 83SCh. 2.4 - Prob. 84SCh. 2.4 - Prob. 85ACh. 2.4 - Prob. 86ACh. 2.4 - Prob. 87ACh. 2.4 - Prob. 88PCh. 2.4 - Prob. 89PCh. 2.4 - Prob. 90PCh. 2.4 - Prob. 91PCh. 2.4 - Prob. 92PCh. 2.4 - Prob. 93PCh. 2.4 - Prob. 94PCh. 2.4 - Prob. 1TFCh. 2.4 - Prob. 2TFCh. 2.4 - Prob. 3TFCh. 2.4 - Prob. 4TFCh. 2.4 - Prob. 5TFCh. 2.4 - Prob. 6TFCh. 2.4 - Prob. 7TFCh. 2.4 - Prob. 8TFCh. 2.4 - Prob. 9TFCh. 2.4 - Prob. 10TFCh. 2.5 - Prob. 1TBCh. 2.5 - Prob. 2TBCh. 2.5 - Prob. 0CCh. 2.5 - 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Prob. 27SCCh. 2 - Prob. 28SCCh. 2 - Prob. 29SCCh. 2 - Prob. 30SCCh. 2 - Prob. 31SCCh. 2 - Prob. 32SCCh. 2 - Prob. 33SCCh. 2 - Prob. 34SCCh. 2 - Prob. 35SCCh. 2 - Prob. 36SCCh. 2 - Prob. 37SCCh. 2 - Prob. 38SCCh. 2 - Prob. 39SCCh. 2 - Prob. 40SCCh. 2 - Prob. 41SCCh. 2 - Prob. 42SCCh. 2 - Prob. 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- In Exercises 83–86, determine whether thestatement is true or false. If it is false, explain why or give anexample that shows it is false. If the graph of a function has three x-intercepts, then it musthave at least two points at which its tangent line is horizontalarrow_forwardUse Definition 0.10 to show that each pair of functions in Exercises 67–70 are inverses of each other. 1 2 67. f(x) =2 – 3x and g(x) = -x+ 3 68. f(x) = x² restricted to [0, 0) and g(x) = V 69. f(x) = and g(x) = 1+x 1-x 1 1 70. f(x) = and g(x) 2x 2xarrow_forwardEach of Exercises 25–36 gives a formula for a function y = f(x). In each case, find f-x) and identify the domain and range of f-. As a check, show that f(fx)) = f-"f(x)) = x. 25. f(x) = x 26. f(x) = x, x20 %3D %3D 27. f(x) = x + 1 28. f(x) = (1/2)x – 7/2 30. f(x) = 1/r, x * 0 %3D 29. f(x) = 1/x, x>0 x + 3 31. f(x) 32. f(x) = VE - 3 34. f(x) = (2x + 1)/5 2 33. f(x) = x - 2r, xs1 (Hint: Complete the square.) * + b x - 2' 35. f(x) = b>-2 and constant 36. f(x) = x? 2bx, b> 0 and constant, xsbarrow_forward
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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