Explanation Given: The function is y = 5 x + 6 x . Rewrite the function as y = 5 x + 6 ( x ) 1 2 . Formula used: (1) The quotient rule is, d d x [ u ( x ) v ( x ) ] = v ( x ) ⋅ u ' ( x ) − u ( x ) ⋅ v ' ( x ) ( v ( x ) ) 2 . (2) The sum or difference rule , d d x ( u ( x ) + v ( x ) ) = d d x ( u ( x ) ) + d d x ( v ( x ) ) . (3) The power rule, d d x ( x n ) = n x n − 1 . (4) The constant rule, d d x ( k ) = 0 . Calculation: The given function is in the quotient form. Apply the quotient rule for the given function. Let u ( x ) = 5 x + 6 and v ( x ) = ( x ) 1 2 . d d x [ 5 x + 6 ( x ) 1 2 ] = ( ( x ) 1 2 ) d d x ( 5 x + 6 ) − ( 5 x + 6 ) d d x ( ( x ) 1 2 ) ( ( x ) 1 2 ) 2 = ( ( x ) 1 2 ) ( d d x ( 5 x ) + d d x ( 6 ) ) − ( 5 x + 6 ) d d x ( ( x ) 1 2 ) ( ( x ) 1 2 ) 2 x

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

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

Publisher: PEARSON

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 12.2, Problem 23E

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To find: The derivative of the given function using the quotient rule.

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Chapter 12.2, Problem 22E

Chapter 12.2, Problem 24E

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Chapter 12 Solutions

Finite Mathematics and Calculus with Applications (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

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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 derivative of the given function using the quotient rule .

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Chapter 12 Solutions