R Functions, Graphs, And Models 1 Differentiation 2 Applications Of Differentiation 3 Exponential And Logarithmic Functions 4 Integration 5 Applications Of Integration 6 Functions Of Several Variables CR Cumulative Review A Review Of Basic Algebra PSDT Prerequisite Skills Diagnostic Test expand_more
1.1 Limits: A Numerical And Graphical Approach 1.2 Algebraic Limits And Continuity 1.3 Average Rates Of Change 1.4 Differentiation Using Limits Of Difference Quotients 1.5 The Power And Sum–difference Rules 1.6 The Product And Quotient Rules 1.7 The Chain Rule 1.8 Higher-order Derivatives Chapter Questions expand_more
Problem 1E: Differentiate each function.
1. (Check by expanding and then differentiating.)
Problem 2E: Differentiate each function. y=(2x+1)2 (Check by expanding and then differentiating.) Problem 3E: Differentiate each function. y=(7x)55 Problem 4E: Differentiate each function.
4.
Problem 5E: Differentiate each function.
5.
Problem 6E: Differentiate each function.
6.
Problem 7E: Differentiate each function. y=3x24 Problem 8E: Differentiate each function.
8.
Problem 9E: Differentiate each function.
9.
Problem 10E: Differentiate each function. y=(8x26)40 Problem 11E: Differentiate each function.
11.
Problem 12E: Differentiate each function. y=(x+5)7(4x1)10 Problem 13E: Differentiate each function. y=1(4x+5)2 Problem 14E: Differentiate each function. y=1(3x+8)2 Problem 15E: Differentiate each function. y=4x2(7+5x)3 Problem 16E: Differentiate each function. y=7x3(49x)5 Problem 17E: Differentiate each function. f(x)=(3+x3)5(1+x7)4 Problem 18E: Differentiate each function.
18.
Problem 19E: Differentiate each function. f(x)=x2+(200x)2 Problem 20E: Differentiate each function. f(x)=x2+(100x)2 Problem 21E: Differentiate each function. G(x)=2x13+(4xx)2 Problem 22E: Differentiate each function.
22.
Problem 23E: Differentiate each function.
23.
Problem 24E: Differentiate each function.
24.
Problem 25E: Differentiate each function.
25.
Problem 26E: Differentiate each function. g(x)=(3x1)7(2x+1)5 Problem 27E: Differentiate each function.
27.
Problem 28E: Differentiate each function. f(x)=x35x+2 Problem 29E: Differentiate each function.
29.
Problem 30E: Differentiate each function.
30.
Problem 31E: Differentiate each function.
31.
Problem 32E: Differentiate each function.
32.
Problem 33E: Differentiate each function. g(x)=3+2x5x Problem 34E: Differentiate each function. g(x)=4x3+x Problem 35E: Differentiate each function. f(x)=(2x33x2+4x+1)100 Problem 36E: Differentiate each function. f(x)=(7x4+6x3x)204 Problem 37E: Differentiate each function.
37.
Problem 38E: Differentiate each function.
38.
Problem 39E: Differentiate each function. f(x)=x2+xx2x Problem 40E: Differentiate each function.
40.
Problem 41E: Differentiate each function. f(x)=(5x4)7(6x+1)3 Problem 42E: Differentiate each function.
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Problem 43E: Differentiate each function. f(x)=12(2x+1)2/3(3x4)5/4 Problem 44E: Differentiate each function. y=6x2+x3(x46x)3 Problem 45E: Find .
45.
Problem 46E: Find .
46.
Problem 47E: Find .
47.
Problem 48E: Find .
48.
Problem 49E: Find dydu,dudx,anddydx. y=(u+1)(u1)andu=x3+1 Problem 50E: Find dydu,dudx,anddydx. y=u(u+1)andu=x32x Problem 51E: Find dydx for each pair of functions. y=5u2+3u,whereu=x3+1 Problem 52E: Find for each pair of functions.
52.
Problem 53E: Find dydx for each pair of functions. y=73u,whereu=x29 Problem 54E: Find dydx for each pair of functions. y=2u+53,whereu=x2x Problem 55E: Find dydx for each pair of functions. Find dydxify=1u2+uandu=5+3t. Problem 56E: Find dydx for each pair of functions. Find dydtify=1u2+uandu=5+3t. Problem 57E: 57. Find an equation for the tangent line to the graph of at the point .
Problem 58E: Find an equation for the tangent line to the graph of y=x2+3x at the point (1,2). Problem 59E: 59. Find an equation for the tangent line to the graph of at the point .
Problem 60E: 60. Find an equation for the tangent line to the graph of at the point .
Problem 61E: Consider g(x)=(6x+12x5)2. a. Find g(x) using the Extended power Rule. b. note that... Problem 62E: 62. Consider
.
a. Find using the Quotient and the Extended Power Rule.
b. Note that . Find ... Problem 63E: 63. Let .
Find .
Problem 64E: Let f(u)=u+1u1andg(x)=u=x. Find (fg)(4). Problem 65E: Let f(u)=u3andg(x)=u=1+3x2. Find (fg)(2). Problem 66E: 66. Let .
Find .
Problem 67E: For Exercises 67-70, Use the chain Rule to differentiate each function. You may need to apply the... Problem 68E: For Exercises 67-70, Use the chain Rule to differentiate each function. You may need to apply the... Problem 69E: For Exercises 67-70, Use the chain Rule to differentiate each function. You may need to apply the... Problem 70E: For Exercises 67-70, Use the chain Rule to differentiate each function. You may need to apply the... Problem 71E: Total revenue. A total-revenue function is given by R(x)=1000x20.1x, where R(x) is the total... Problem 72E: Total cost. A total-cost function is given by C(x)=2000(x2+2)1/3+700, where C(x) is the total cost,... Problem 73E: 73. Total profit. Use the total-cost and total revenue functions in Exercises 71 and 72 to find the... Problem 74E: 74. Total cost. A company determine that its total cost, in thousands of dollars, for producing, for... Problem 75E: Consumer credit. The total outstanding consumer credit of the united states (in billions of dollars)... Problem 76E: Utility. Utility is a type of function that occurs in economics. When a consumer receives x units of... Problem 77E: Compound interest. If 1000 is invested at interest rate r, compounded quarterly, 5 yr it will grow... Problem 78E: Compound interest. If 1000 is invested at interest rate r compared annually, in 3 yr it will grow to... Problem 79E: 79. Business profit. French’s Electronics is selling laptop computers. It determines that its total... Problem 80E: Consumer demand. Suppose the demand function for a new autobiography is given by D(p)=80,000p, and... Problem 81E: Chemotherapy. The dosage for Carboplatin chemotherapy drugs depends on several parameters for the... Problem 82E: If f(x) is a function, then (f)(x)=f(f(x)) is the composition of f with itself. This is called an... Problem 83E: If f(x) is a function, then (f)(x)=f(f(x)) is the composition of f with itself. This is called an... Problem 84E: If is a function, then is the composition of with itself. This is called an iterated function,... Problem 85E: If f(x) is a function, then (f)(x)=f(f(x)) is the composition of f with itself. This is called an... Problem 86E: Differentiate. y=(2x3)3+1 Problem 87E: Differentiate.
87.
Problem 88E: Differentiate. y=(xx1)3 Problem 89E Problem 90E: Differentiate. y=1x21x Problem 91E: Differentiate. y=(x2x1x2+1)3 Problem 92E: Differentiate.
92.
Problem 93E Problem 94E Problem 95E: 95. The Extended Power Rule (for positive integer powers can be verified using the Product Rule. For... Problem 96E: 96. The following is the beginning of an alternative proof of the Quotient Rule that uses the... Problem 97E: For the function in each of Exercises 97 and 98, graph and over the given interval. Then estimate... Problem 98E: For the function in each of Exercises 97 and 98, graph f and f over the given interval. Then... Problem 99E Problem 100E: Find the derivative of each of the following function functions. Then use a calculate to check the... format_list_bulleted