1 Functions 2 Limits And Continuity 3 Derivatives 4 Application Of Derivatives 5 Integrals 6 Applications Of Definite Integrals 7 Trascendental Functions 8 Techniques Of Integration 9 First-order Differential Equations 10 Infinite Sequences And Series 11 Parametric Equations And Polar Coordinates 12 Vectors And The Geometry Of Space 13 Vector-valued Functions And Motion In Space 14 Partial Derivatives 15 Multiple Integrals 16 Integrals And Vector Fields 17 Second-order Differential Equations A.1 Real Numbers And The Real Line A.2 Mathematical Induction A.3 Lines, Circles, And Parabolas A.4 Proofs Of Limit Theorems A.5 Commonly Occurring Limits A.6 Theory Of The Real Numbers A.7 Complex Numbers A.8 The Distributive Law For Vector Cross Products A.9 The Mixed Derivative Theorem And The Increment Theorem expand_more
3.1 Tangent Lines And The Derivative At A Point 3.2 The Derivative As A Function 3.3 Differentiation Rules 3.4 The Derivative As A Rate Of Change 3.5 Derivatives Of Trigonometric Functions 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Related Rates 3.9 Linearization And Differentials Chapter Questions expand_more
Problem 1E: Derivative Calculations
In Exercises 1–8, given y = f(u) and u = g(x), find dy/dx = dy/dx =... Problem 2E: Derivative Calculations
In Exercises 1–8, given y = f(u) and u = g(x), find dy/dx = dy/dx =... Problem 3E: Derivative Calculation
In Exercises 1–8, given y = f(u) and u = g(x), find dy/dx = dy/dx =... Problem 4E Problem 5E Problem 6E: Derivation Calculations
In Exercises 1–8, given y = f(u) and u = g(x), find dy/dx = dy/dx =... Problem 7E Problem 8E Problem 9E: In Exercises 9–22, write the function in the form y = f(u) and u = g(x). Then find dy/dx as a... Problem 10E: In Exercises 9–22, write the function in the form y = f(u) and u = g(x). Then find dy/dx as a... Problem 11E: In Exercises 9–22, write the function in the form y = f(u) and u = g(x). Then find dy/dx as a... Problem 12E: In Exercises 9–22, write the function in the form y = f(u) and u = g(x). Then find dy/dx as a... Problem 13E: In Exercises 9–22, write the function in the form y = f(u) and u = g(x). Then find dy/dx as a... Problem 14E: In Exercises 9–22, write the function in the form y = f(u) and u = g(x). Then find dy/dx as a... Problem 15E: In Exercises 9–22, write the function in the form y = f(u) and u = g(x). Then find dy/dx as a... Problem 16E: In Exercises 9–22, write the function in the form y = f(u) and u = g(x). Then find dy/dx as a... Problem 17E: In Exercises 9–22, write the function in the form y = f(u) and u = g(x). Then find dy/dx as a... Problem 18E Problem 19E: Find the derivatives of the functions in Exercises 23–50.
23.
Problem 20E: Find the derivatives of the functions in Exercises 23–50.
24.
Problem 21E Problem 22E Problem 23E: Find the derivatives of the functions in Exercises 23–50.
27. r = (csc θ + cot θ)−1
Problem 24E: Find the derivatives of the functions in Exercises 23–50.
28. r = 6(sec θ − tan θ)3/2
Problem 25E Problem 26E: Find the derivatives of the functions in Exercises 23–50.
30.
Problem 27E Problem 28E: Find the derivatives of the functions in Exercises 23–50.
32.
Problem 29E: Find the derivatives of the functions in Exercises 23–50.
33. y = (4x + 3)4(x + 1)−3
Problem 30E: Find the derivatives of the functions in Exercises 23–50.
34. y = (2x − 5)−1(x2 – 5x)6
Problem 31E Problem 32E Problem 33E: Find the derivatives of the functions in Exercises 23–50.
41.
Problem 34E: Find the derivatives of the functions in Exercises 23–50.
42.
Problem 35E: Find the derivatives of the functions in Exercises 23–50.
43.
Problem 36E Problem 37E Problem 38E Problem 39E Problem 40E: Find the derivatives of the functions in Exercises 23–50.
48.
Problem 41E: In Exercises 51–70, find dy/dt.
51. y = sin2(πt − 2)
Problem 42E: In Exercises 51–70, find dy/dt.
52. y = sec2 πt
Problem 43E Problem 44E: In Exercises 51–70, find dy/dt.
54. y = (1 + cot (t/2))−2
Problem 45E Problem 46E: In Exercises 51–70, find dy/dt.
56. y = (t−3/4 sin t)4/3
Problem 47E: In Exercises 51–70, find dy/dt.
59.
Problem 48E: In Exercises 51–70, find dy/dt.
60.
Problem 49E: In Exercises 51–70, find dy/dt.
61. y = sin (cos (2t − 5))
Problem 50E: In Exercises 51–70, find dy/dt.
62.
Problem 51E: In Exercises 51–70, find dy/dt.
63.
Problem 52E Problem 53E Problem 54E Problem 55E Problem 56E: In Exercises 51–70, find dy/dt.
68. y = cos4(sec2 3t)
Problem 57E: In Exercises 51–70, find dy/dt.
69. y = 3t(2t2 − 5)4
Problem 58E: In Exercises 51–70, find dy/dt.
70.
Problem 59E: Second Derivatives
Find y″ in Exercises 71–78.
71.
Problem 60E Problem 61E: Second Derivatives
Find y″ in Exercises 71–78.
73.
Problem 62E: Second Derivatives
Find y″ in Exercises 71–78.
74.
Problem 63E Problem 64E: Second Derivatives
Find y″ in Exercises 71–78.
76. y = x2(x3 − l)5
Problem 65E: For each of the following functions, solve both f′(x) = 0 and f″(x) = 0 for x.
f(x) = x(x − 4)3
Problem 66E Problem 67E: Finding Derivative values
In Exercises 81–86, find the value of (f ◦ g)′ at the given value of... Problem 68E Problem 69E Problem 70E Problem 71E: Finding Derivative values
In Exercises 81–86, find the value of (f ◦ g)′ at the given value of... Problem 72E: Finding Derivative values
In Exercises 81–86, find the value of (f ◦ g)′ at the given value of... Problem 73E: Assume that f′(3) = −1, g′(2) = 5, g(2) = 3, and y = f(g(x)). What is y′ at x = 2?
Problem 74E Problem 75E: Suppose that functions f and g and their derivatives with respect to x have the following values at... Problem 76E: Suppose that the functions f and g and their derivatives with respect to x have the following values... Problem 77E Problem 78E Problem 79E Problem 80E: What happens if you can write a function as a composition in different ways? Do you get the... Problem 81E: Find the tangent line to at x= 0.
Problem 82E: Find the tangent line to at x = 2.
Problem 83E Problem 84E Problem 85E: Suppose that a piston is moving straight up and down and that its position at time t sec is
with A... Problem 86E Problem 87E Problem 88E: Suppose that the velocity of a falling body is m/sec (k a constant) at the instant the body has... Problem 89E Problem 90E: A particle moves along the x-axis with velocity dx/ dt = f (x). Show that the particle’ s... Problem 91E Problem 92E Problem 93E Problem 94E Problem 95E Problem 96E Problem 97E: Consider the function
Show that f is continuous at x = 0.
Determine f ' for x 0.
Show that f is... Problem 98E Problem 99E: Verify each of the following statements.
If f is even, then f ' is odd.
If f is odd, then f ' is... Problem 100E Problem 101E: (Continuation of Exercise 100.) In Exercise 100, the trigonometric polynomial ƒ(t) that approximated... format_list_bulleted