(a) Explanation Given: x 1 2 3 4 f ( x ) 3 4 2 1 f ′ ( x ) − 5 − 6 − 7 − 11 g ( x ) 4 1 2 3 g ′ ( x ) 2 9 3 10 4 11 6 13 Calculation: Use Chain rule and obtain the value of D x ( f [ g ( x ) ] ) as follows. D x ( f [ g ( x ) ] ) = d d x ( f [ g ( x ) ] ) = f ′ [ g ( x ) ] d d x ( g ( x ) ) = f ′ [ g ( x ) ] g ′ ( x ) Thus, D x ( f [ g ( x ) ] ) at x = (b) To determine To find: The value of D x ( f [ g ( x ) ] ) at x = 3 .

Finite Mathematics and Calculus with Applications Books a la Carte Plus MyLab Math Package (10th Edition)

10th Edition

ISBN: 9780133935592

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 12, Problem 51RE

(a)

To determine

To find: The value of Dx(f[g(x)]) at x=2 .

(b)

To determine

To find: The value of Dx(f[g(x)]) at x=3 .

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Chapter 12, Problem 50RE

Chapter 12, Problem 52RE

Chapter 12 Solutions

Finite Mathematics and Calculus with Applications Books a la Carte Plus MyLab Math Package (10th Edition)

Ch. 12.1 - iff(t)=1t, find f(t).Ch. 12.1 - Prob. 2YT Ch. 12.1 - Prob. 3YT Ch. 12.1 - If the cost function is given by C(x) = 5x3 10x2...Ch. 12.1 - Prob. 5YT Ch. 12.1 - Prob. 1WE Ch. 12.1 - Prob. 2WE Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E Ch. 12.1 - Prob. 9E Ch. 12.1 - Prob. 10E Ch. 12.1 - Prob. 11E Ch. 12.1 - Prob. 12E Ch. 12.1 - Prob. 13E Ch. 12.1 - Prob. 14E Ch. 12.1 - Prob. 15E Ch. 12.1 - Prob. 16E Ch. 12.1 - Prob. 17E Ch. 12.1 - Prob. 18E Ch. 12.1 - Prob. 19E Ch. 12.1 - Prob. 20E Ch. 12.1 - Prob. 21E Ch. 12.1 - Prob. 22E Ch. 12.1 - Prob. 23E Ch. 12.1 - Prob. 24E Ch. 12.1 - Prob. 25E Ch. 12.1 - Prob. 26E Ch. 12.1 - Prob. 27E Ch. 12.1 - Prob. 28E Ch. 12.1 - Prob. 29E Ch. 12.1 - Prob. 30E Ch. 12.1 - Prob. 31E Ch. 12.1 - Prob. 32E Ch. 12.1 - Prob. 33E Ch. 12.1 - Prob. 34E Ch. 12.1 - Prob. 35E Ch. 12.1 - Prob. 36E Ch. 12.1 - Prob. 37E Ch. 12.1 - Prob. 38E Ch. 12.1 - Prob. 39E Ch. 12.1 - Prob. 40E Ch. 12.1 - Prob. 41E Ch. 12.1 - Prob. 42E Ch. 12.1 - Prob. 43E Ch. 12.1 - Prob. 44E Ch. 12.1 - Prob. 45E Ch. 12.1 - Prob. 46E Ch. 12.1 - Prob. 47E Ch. 12.1 - Prob. 48E Ch. 12.1 - Prob. 49E Ch. 12.1 - Prob. 50E Ch. 12.1 - RevenueAssume that a demand equation is given by q...Ch. 12.1 - Prob. 52E Ch. 12.1 - Prob. 53E Ch. 12.1 - Prob. 54E Ch. 12.1 - Prob. 55E Ch. 12.1 - Prob. 56E Ch. 12.1 - Prob. 57E Ch. 12.1 - Prob. 58E Ch. 12.1 - Prob. 59E Ch. 12.1 - Prob. 60E Ch. 12.1 - Prob. 61E Ch. 12.1 - Prob. 62E Ch. 12.1 - Prob. 63E Ch. 12.1 - Prob. 64E Ch. 12.1 - Track and FieldIn 1906 Kennelly developed a simple...Ch. 12.1 - Human CoughTo increase the velocity of the air...Ch. 12.1 - Prob. 67E Ch. 12.1 - Prob. 68E Ch. 12.1 - Prob. 69E Ch. 12.1 - Prob. 70E Ch. 12.1 - Prob. 71E Ch. 12.1 - Prob. 72E Ch. 12.1 - VelocityA ball is thrown vertically upward from...Ch. 12.1 - Prob. 74E Ch. 12.1 - Prob. 75E Ch. 12.1 - Prob. 76E Ch. 12.1 - Dogs Human AgeFrom the data printed in the...Ch. 12.2 - Prob. 1YT Ch. 12.2 - Prob. 2YT Ch. 12.2 - Prob. 3YT Ch. 12.2 - Prob. 4YT Ch. 12.2 - Prob. 1WE Ch. 12.2 - Prob. 2WE Ch. 12.2 - Prob. 3WE Ch. 12.2 - Prob. 1E Ch. 12.2 - Prob. 2E Ch. 12.2 - Prob. 3E Ch. 12.2 - Prob. 4E Ch. 12.2 - Prob. 5E Ch. 12.2 - Prob. 6E Ch. 12.2 - Prob. 7E Ch. 12.2 - Prob. 8E Ch. 12.2 - Prob. 9E Ch. 12.2 - Prob. 10E Ch. 12.2 - Prob. 11E Ch. 12.2 - Prob. 12E Ch. 12.2 - Prob. 13E Ch. 12.2 - Prob. 14E Ch. 12.2 - Prob. 15E Ch. 12.2 - Prob. 16E Ch. 12.2 - Prob. 17E Ch. 12.2 - Prob. 18E Ch. 12.2 - Prob. 19E Ch. 12.2 - Prob. 20E Ch. 12.2 - Prob. 21E Ch. 12.2 - Prob. 22E Ch. 12.2 - Prob. 23E Ch. 12.2 - Prob. 24E Ch. 12.2 - Prob. 25E Ch. 12.2 - Prob. 26E Ch. 12.2 - Prob. 27E Ch. 12.2 - Prob. 28E Ch. 12.2 - Prob. 29E Ch. 12.2 - Prob. 30E Ch. 12.2 - Prob. 31E Ch. 12.2 - Prob. 32E Ch. 12.2 - Prob. 33E Ch. 12.2 - Prob. 34E Ch. 12.2 - Prob. 35E Ch. 12.2 - Prob. 36E Ch. 12.2 - Prob. 37E Ch. 12.2 - Prob. 38E Ch. 12.2 - Prob. 39E Ch. 12.2 - Prob. 40E Ch. 12.2 - Prob. 41E Ch. 12.2 - There are special cases in which the derivative of...Ch. 12.2 - Prob. 43E Ch. 12.2 - Prob. 44E Ch. 12.2 - Employee TrainingA company that manufactures...Ch. 12.2 - Prob. 46E Ch. 12.2 - Prob. 47E Ch. 12.2 - Prob. 48E Ch. 12.2 - Average CostA gasoline refinery found that the...Ch. 12.2 - Prob. 50E Ch. 12.2 - Prob. 51E Ch. 12.2 - Prob. 52E Ch. 12.2 - Prob. 53E Ch. 12.2 - Memory RetentionSome psychologists contend that...Ch. 12.2 - Prob. 55E Ch. 12.2 - Prob. 56E Ch. 12.3 - Prob. 1YT Ch. 12.3 - Prob. 2YT Ch. 12.3 - Prob. 3YT Ch. 12.3 - Prob. 4YT Ch. 12.3 - Prob. 5YT Ch. 12.3 - Prob. 6YT Ch. 12.3 - Prob. 7YT Ch. 12.3 - Prob. 1WE Ch. 12.3 - Prob. 2WE Ch. 12.3 - Prob. 3WE Ch. 12.3 - Prob. 1E Ch. 12.3 - Prob. 2E Ch. 12.3 - Prob. 3E Ch. 12.3 - Prob. 4E Ch. 12.3 - Prob. 5E Ch. 12.3 - Prob. 6E Ch. 12.3 - Prob. 7E Ch. 12.3 - Prob. 8E Ch. 12.3 - Prob. 9E Ch. 12.3 - Prob. 10E Ch. 12.3 - Prob. 11E Ch. 12.3 - Prob. 12E Ch. 12.3 - Prob. 13E Ch. 12.3 - Prob. 14E Ch. 12.3 - Prob. 15E Ch. 12.3 - Prob. 16E Ch. 12.3 - Prob. 17E Ch. 12.3 - Prob. 18E Ch. 12.3 - Prob. 19E Ch. 12.3 - Prob. 20E Ch. 12.3 - Prob. 21E Ch. 12.3 - Prob. 22E Ch. 12.3 - Prob. 23E Ch. 12.3 - Prob. 24E Ch. 12.3 - Prob. 25E Ch. 12.3 - Prob. 26E Ch. 12.3 - Prob. 27E Ch. 12.3 - Prob. 28E Ch. 12.3 - Prob. 29E Ch. 12.3 - Prob. 30E Ch. 12.3 - Prob. 31E Ch. 12.3 - Prob. 32E Ch. 12.3 - Prob. 33E Ch. 12.3 - Prob. 34E Ch. 12.3 - Prob. 35E Ch. 12.3 - Prob. 36E Ch. 12.3 - Prob. 37E Ch. 12.3 - Prob. 38E Ch. 12.3 - Prob. 39E Ch. 12.3 - Prob. 40E Ch. 12.3 - Prob. 41E Ch. 12.3 - Prob. 42E Ch. 12.3 - Prob. 43E Ch. 12.3 - Prob. 44E Ch. 12.3 - Prob. 45E Ch. 12.3 - Prob. 46E Ch. 12.3 - Prob. 47E Ch. 12.3 - Prob. 48E Ch. 12.3 - Prob. 49E Ch. 12.3 - Prob. 50E Ch. 12.3 - Prob. 51E Ch. 12.3 - Prob. 52E Ch. 12.3 - Prob. 53E Ch. 12.3 - Prob. 54E Ch. 12.3 - Prob. 55E Ch. 12.3 - Prob. 56E Ch. 12.3 - Prob. 57E Ch. 12.3 - Prob. 58E Ch. 12.3 - Prob. 59E Ch. 12.3 - Prob. 60E Ch. 12.3 - Prob. 61E Ch. 12.3 - Prob. 62E Ch. 12.3 - Prob. 63E Ch. 12.3 - Prob. 64E Ch. 12.4 - Prob. 1YT Ch. 12.4 - Prob. 2YT Ch. 12.4 - Prob. 3YT Ch. 12.4 - Prob. 4YT Ch. 12.4 - Prob. 1WE Ch. 12.4 - Prob. 2WE Ch. 12.4 - Prob. 3WE Ch. 12.4 - Prob. 1E Ch. 12.4 - Prob. 2E Ch. 12.4 - Prob. 3E Ch. 12.4 - Prob. 4E Ch. 12.4 - Prob. 5E Ch. 12.4 - Prob. 6E Ch. 12.4 - Prob. 7E Ch. 12.4 - Prob. 8E Ch. 12.4 - Prob. 9E Ch. 12.4 - Prob. 10E Ch. 12.4 - Prob. 11E Ch. 12.4 - Prob. 12E Ch. 12.4 - Prob. 13E Ch. 12.4 - Prob. 14E Ch. 12.4 - Prob. 15E Ch. 12.4 - Prob. 16E Ch. 12.4 - Prob. 17E Ch. 12.4 - Prob. 18E Ch. 12.4 - Prob. 19E Ch. 12.4 - Prob. 20E Ch. 12.4 - Prob. 21E Ch. 12.4 - Prob. 22E Ch. 12.4 - Prob. 23E Ch. 12.4 - Prob. 24E Ch. 12.4 - Prob. 25E Ch. 12.4 - Prob. 26E Ch. 12.4 - Prob. 27E Ch. 12.4 - Prob. 28E Ch. 12.4 - Prob. 29E Ch. 12.4 - Prob. 30E Ch. 12.4 - Prob. 31E Ch. 12.4 - Prob. 32E Ch. 12.4 - Prob. 33E Ch. 12.4 - Prob. 34E Ch. 12.4 - Prob. 35E Ch. 12.4 - Prob. 36E Ch. 12.4 - Prob. 37E Ch. 12.4 - Prob. 38E Ch. 12.4 - Prob. 39E Ch. 12.4 - Prob. 40E Ch. 12.4 - Franchising Marketing researchers have studied the...Ch. 12.4 - Prob. 42E Ch. 12.4 - Prob. 43E Ch. 12.4 - Prob. 44E Ch. 12.4 - Life Sciences 45. Minority Population In Section...Ch. 12.4 - Population Growth In Section 10.4, Exercise 49,...Ch. 12.4 - Cactus Wrens The weight of cactus wrens in grams...Ch. 12.4 - Prob. 48E Ch. 12.4 - Prob. 49E Ch. 12.4 - Prob. 50E Ch. 12.4 - Prob. 52E Ch. 12.4 - Prob. 53E Ch. 12.4 - Prob. 54E Ch. 12.4 - Prob. 55E Ch. 12.4 - Prob. 56E Ch. 12.4 - Prob. 57E Ch. 12.4 - Physical Sciences 58. Radioactive Decay The amount...Ch. 12.4 - Prob. 59E Ch. 12.4 - Prob. 60E Ch. 12.4 - Prob. 61E Ch. 12.4 - Prob. 62E Ch. 12.4 - Prob. 63E Ch. 12.4 - Prob. 64E Ch. 12.4 - Track and Field In 1958, L. Lucy developed a...Ch. 12.5 - Prob. 1YT Ch. 12.5 - Prob. 2YT Ch. 12.5 - Prob. 3YT Ch. 12.5 - Prob. 1WE Ch. 12.5 - Prob. 2WE Ch. 12.5 - Prob. 3WE Ch. 12.5 - Prob. 1E Ch. 12.5 - Prob. 2E Ch. 12.5 - Prob. 3E Ch. 12.5 - Prob. 4E Ch. 12.5 - Prob. 5E Ch. 12.5 - Prob. 6E Ch. 12.5 - Prob. 7E Ch. 12.5 - Prob. 8E Ch. 12.5 - Prob. 9E Ch. 12.5 - Prob. 10E Ch. 12.5 - Prob. 11E Ch. 12.5 - Prob. 12E Ch. 12.5 - Prob. 13E Ch. 12.5 - Prob. 14E Ch. 12.5 - Prob. 15E Ch. 12.5 - Prob. 16E Ch. 12.5 - Prob. 17E Ch. 12.5 - Prob. 18E Ch. 12.5 - Prob. 19E Ch. 12.5 - Prob. 20E Ch. 12.5 - Prob. 21E Ch. 12.5 - Prob. 22E Ch. 12.5 - Prob. 23E Ch. 12.5 - Prob. 24E Ch. 12.5 - Prob. 25E Ch. 12.5 - Prob. 26E Ch. 12.5 - Prob. 27E Ch. 12.5 - Prob. 28E Ch. 12.5 - Prob. 29E Ch. 12.5 - Prob. 30E Ch. 12.5 - Find the derivative of each of the following...Ch. 12.5 - Prob. 32E Ch. 12.5 - Prob. 33E Ch. 12.5 - Prob. 34E Ch. 12.5 - Prob. 35E Ch. 12.5 - Prob. 36E Ch. 12.5 - Prob. 37E Ch. 12.5 - Prob. 38E Ch. 12.5 - Prob. 39E Ch. 12.5 - Prob. 40E Ch. 12.5 - Prob. 41E Ch. 12.5 - Prob. 42E Ch. 12.5 - Prob. 43E Ch. 12.5 - Prob. 44E Ch. 12.5 - Prob. 45E Ch. 12.5 - Prob. 46E Ch. 12.5 - Prob. 47E Ch. 12.5 - Prob. 48E Ch. 12.5 - Prob. 49E Ch. 12.5 - Prob. 50E Ch. 12.5 - Prob. 51E Ch. 12.5 - Prob. 52E Ch. 12.5 - Prob. 53E Ch. 12.5 - Prob. 54E Ch. 12.5 - Prob. 55E Ch. 12.5 - Prob. 56E Ch. 12.5 - Prob. 57E Ch. 12.5 - Profit If the cost function in dollars for q units...Ch. 12.5 - Prob. 59E Ch. 12.5 - Prob. 60E Ch. 12.5 - Prob. 61E Ch. 12.5 - Prob. 62E Ch. 12.5 - Fruit Flies A study of the relation between the...Ch. 12.5 - Prob. 64E Ch. 12.5 - Prob. 65E Ch. 12.5 - Prob. 66E Ch. 12.5 - Prob. 67E Ch. 12.5 - Prob. 68E Ch. 12 - Determine whether each of the following statements...Ch. 12 - Determine whether each of the following statements...Ch. 12 - Prob. 3RE Ch. 12 - Prob. 4RE Ch. 12 - Prob. 5RE Ch. 12 - Prob. 6RE Ch. 12 - Prob. 7RE Ch. 12 - Prob. 8RE Ch. 12 - Prob. 9RE Ch. 12 - Determine whether each of the following statements...Ch. 12 - Prob. 11RE Ch. 12 - Prob. 12RE Ch. 12 - Prob. 13RE Ch. 12 - Prob. 14RE Ch. 12 - Prob. 15RE Ch. 12 - Prob. 16RE Ch. 12 - Prob. 17RE Ch. 12 - Prob. 18RE Ch. 12 - Prob. 19RE Ch. 12 - Prob. 20RE Ch. 12 - Prob. 21RE Ch. 12 - Prob. 22RE Ch. 12 - Prob. 23RE Ch. 12 - Prob. 24RE Ch. 12 - Prob. 25RE Ch. 12 - Prob. 26RE Ch. 12 - Prob. 27RE Ch. 12 - Prob. 28RE Ch. 12 - Prob. 29RE Ch. 12 - Prob. 30RE Ch. 12 - Prob. 31RE Ch. 12 - Prob. 32RE Ch. 12 - Prob. 33RE Ch. 12 - Prob. 34RE Ch. 12 - Prob. 35RE Ch. 12 - Prob. 36RE Ch. 12 - Prob. 37RE Ch. 12 - Prob. 38RE Ch. 12 - Prob. 39RE Ch. 12 - Prob. 40RE Ch. 12 - Prob. 41RE Ch. 12 - Prob. 42RE Ch. 12 - Prob. 43RE Ch. 12 - Prob. 44RE Ch. 12 - Prob. 45RE Ch. 12 - Prob. 46RE Ch. 12 - Prob. 47RE Ch. 12 - Prob. 48RE Ch. 12 - Prob. 49RE Ch. 12 - Prob. 50RE Ch. 12 - Prob. 51RE Ch. 12 - Prob. 52RE Ch. 12 - Prob. 53RE Ch. 12 - Prob. 54RE Ch. 12 - Prob. 55RE Ch. 12 - Prob. 56RE Ch. 12 - Prob. 57RE Ch. 12 - Prob. 58RE Ch. 12 - Prob. 59RE Ch. 12 - Prob. 60RE Ch. 12 - Find the slope of the tangent line to the given...Ch. 12 - Prob. 62RE Ch. 12 - Prob. 63RE Ch. 12 - Prob. 64RE Ch. 12 - Prob. 65RE Ch. 12 - Prob. 66RE Ch. 12 - In Exercise 42 in Section 12.2, we saw an example...Ch. 12 - Prob. 68RE Ch. 12 - Prob. 69RE Ch. 12 - Prob. 70RE Ch. 12 - Prob. 71RE Ch. 12 - Prob. 72RE Ch. 12 - Prob. 73RE Ch. 12 - Prob. 74RE Ch. 12 - Prob. 75RE Ch. 12 - Prob. 76RE Ch. 12 - Prob. 77RE Ch. 12 - Prob. 78RE Ch. 12 - Prob. 79RE Ch. 12 - Prob. 80RE Ch. 12 - Prob. 81RE Ch. 12 - Prob. 83RE Ch. 12 - Prob. 84RE Ch. 12 - Prob. 85RE Ch. 12 - Prob. 86RE Ch. 12 - Prob. 87RE Ch. 12 - Prob. 88RE Ch. 12 - Wind Energy In Section 10.4, Exercise 55, we found...Ch. 12 - Prob. 90RE Ch. 12 - Food Surplus In Section 10.4, Example 7, we found...Ch. 12 - Prob. 92RE Ch. 12 - Prob. 93RE

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The value of D x ( f [ g ( x ) ] ) at x = 2 .

Solution Summary: The author explains how to find the value of D_xleft at x=2.

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To find: The value of Dx(f[g(x)]) at x=2 .

To find: The value of Dx(f[g(x)]) at x=3 .

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Chapter 12 Solutions