1 Functions 2 Limits 3 Derivatives 4 Applications Of The Derivative 5 Integration 6 Applications Of Integration 7 Logarithmic And Exponential, And Hyperbolic Functions 8 Integration Techniques 9 Differential Equations 10 Sequences And Infinite Series 11 Power Series 12 Parametric And Polar Curves 13 Vectors And The Geometry Of Space 14 Vector-valued Functions 15 Functions Of Several Variables 16 Multiple Integration 17 Vector Calculus A Proofs Of Selected Theorems B Algebra Review C Complex Numbers expand_more
3.1 Introducing The Derivatives 3.2 The Derivative As A Function 3.3 Rules Of Differentiation 3.4 The Product And Quotient Rules 3.5 Derivatives Of Trigonometric Functions 3.6 Derivatives As A Rates Of Change 3.7 The Chain Rule 3.8 Implicit Differentiation 3.9 Derivatives Of Logarithmic And Exponential Functions 3.10 Derivatives Of Inverse Trigonometric Functions 3.11 Related Rates Chapter Questions expand_more
Problem 1QC: Find the values of ddx(11) and ddx() Problem 2QC: Use the graph of y = x to give a geometric explanation of why ddx(x)=1. Problem 3QC Problem 4QC: Find the derivative of f(x)=4ex3x2. Problem 5QC: Determine the point(s) at which f(x) = x3 12x has a horizontal tangent line. Problem 6QC Problem 1E: Assume the derivatives of f and g exist in Exercises 16. 1. If the limit definition of a derivative... Problem 2E: Assume the derivatives of f and g exist in Exercises 16. 2. In this section, we showed that the rule... Problem 3E: Assume the derivatives of f and g exist in Exercises 16. 3. Give a nonzero function that is its own... Problem 4E Problem 5E: Assume the derivatives of f and g exist in Exercises 16. 5. How do you find the derivative of a... Problem 6E Problem 7E: Given that f(3) = 6 and g(3) = 2, find (f + g)(3). Problem 8E: If f(0)=6 and g(x)=f(x)+ex+1, find g(0). Problem 9E: Let F(x)=f(x)+g(x),G(x)=f(x)g(x), and H(x)=3f(x)+2g(x), where the graphs of f and g are shown in the... Problem 10E: Let F(x)=f(x)+g(x),G(x)=f(x)g(x), and H(x)=3f(x)+2g(x), where the graphs of f and g are shown in the... Problem 11E: Let F(x)=f(x)+g(x),G(x)=f(x)g(x), and H(x)=3f(x)+2g(x), where the graphs of f and g are shown in the... Problem 12E: Derivatives from a table Use the table to find the following derivatives. 58. ddx(f(x)+g(x))|x=1 Problem 13E: Derivatives from a table Use the table to find the following derivatives. 59. ddx(1.5f(x))|x=2 Problem 14E: Derivatives from a table Use the table to find the following derivatives. 60. ddx(2x3g(x))|x=4 Problem 15E: If f(t)=t10, find f(t),f(t), and f(t). Problem 16E: Find an equation of the line tangent to the graph of y = ex at x = 0. Problem 17E: The line tangent to the graph of f at x = 5 is y=110x2. Find ddx(4f(x))|x=5 Problem 18E: The line tangent to the graph of f at x = 3 is y = 4x 2 and the line tangent to the graph of g at... Problem 19E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 20E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 21E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 22E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 23E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 24E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 25E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 26E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 27E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 28E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 29E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 30E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 31E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 32E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 33E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 34E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 35E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 36E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 37E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 38E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 39E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 40E: Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the... Problem 41E: Height estimate The distance an object falls (when released from rest, under the influence of Earth... Problem 42E: Projectile trajectory The position of a small rocket that is launched vertically upward is given by... Problem 43E: City urbanization City planners model the size of their city using the function A(t)=150t2+2t+20.... Problem 44E: Cell growth When observations begin at t = 0, a cell culture has 1200 cells and continues to grow... Problem 45E: Weight of Atlantic salmon The weight w(x) (in pounds) of an Atlantic salmon that is x inches long... Problem 46E: Derivatives of products and quotients Find the derivative of the following functions by first... Problem 47E: Derivatives of products Find the derivative of the following functions by first expanding the... Problem 48E: Derivatives of products Find the derivative of the following functions by first expanding the... Problem 49E: Derivatives of products Find the derivative of the following functions by first expanding the... Problem 50E: Derivatives of products Find the derivative of the following functions by first expanding the... Problem 51E: Derivatives of products and quotients Find the derivative of the following functions by first... Problem 52E: Derivatives of products and quotients Find the derivative of the following functions by first... Problem 53E: Derivatives of products Find the derivative of the following functions by first expanding the... Problem 54E: Derivatives of products Find the derivative of the following functions by first expanding the... Problem 55E: Derivatives of products Find the derivative of the following functions by first expanding the... Problem 56E: Derivatives of products Find the derivative of the following functions by first expanding the... Problem 57E: Derivatives of products and quotients Find the derivative of the following functions by first... Problem 58E: Derivatives of products and quotients Find the derivative of the following functions by first... Problem 59E: Equations of tangent lines a. Find an equation of the line tangent to the given curve at a. b. Use a... Problem 60E: Equations of tangent lines a. Find an equation of the line tangent to the given curve at a. b. Use a... Problem 61E: Equations of tangent lines a. Find an equation of the line tangent to the given curve at a. b. Use a... Problem 62E: Equations of tangent lines a. Find an equation of the line tangent to the given curve at a. b. Use a... Problem 63E: Finding slope locations Let f(x) = x3 6x + 5. a. Find the values of x for which the slope of the... Problem 64E: Finding slope locations Let f(t) = t3 27t + 5. a. Find the values if t for which the slope of the... Problem 65E: Finding slope locations Let f(x) = 2x3 3x2 12x + 4. a. Find all points on the graph of f at which... Problem 66E: Finding slope locations Let f(x) = 2ex 6x. a. Find all points on the graph of f at which the... Problem 67E: Finding slope locations Let f(x)=4xx. a. Find all points on the graph of f at which the tangent line... Problem 68E: Higher-order derivatives Find f(x), f(x), and f(x) for the following functions. 44. f(x) = 3x3 + 5x2... Problem 69E: Higher-order derivatives Find f(x), f(x), and f(x) for the following functions. 45. f(x) = 5x4 +... Problem 70E: Higher-order derivatives Find f(x), f(x), and f(x) for the following functions. 46. f(x) = 3x2 + 5ex Problem 71E: Higher-order derivatives Find f(x), f(x), and f(x) for the following functions. 47. f(x)=x27x8x+1 Problem 72E: Higher-order derivatives Find f(x), f(x), and f(x) for the following functions. 48. f(x) = 10ex Problem 73E: Explain why or why not Determine whether the following statements are true and give an explanation... Problem 74E: Tangent lines Suppose f(3) = 1 and f(3) = 4. Let g(x) = x2 + f(x) and h(x) = 3f(x). a. Find an... Problem 75E: Derivatives from tangent lines Suppose the line tangent to the graph of f at x = 2 is y = 4x + 1 and... Problem 76E: Tangent line Find the equation of the line tangent to the curve y=x+x that has slope 2. Problem 77E: Tangent line given Determine the constants b and c such that the line tangent to f(x) = x2 + bx + c... Problem 78E: Derivatives from a graph Let F = f + g and G = 3f g, where the graphs of f and g are shown in the... Problem 79E: Derivatives from a graph Let F = f + g and G = 3f g, where the graphs of f and g are shown in the... Problem 80E: Derivatives from a graph Let F = f + g and G = 3f g, where the graphs of f and g are shown in the... Problem 81E: Derivatives from a graph Let F = f + g and G = 3f g, where the graphs of f and g are shown in the... Problem 82E: Derivatives from limits The following limits represent f(a) for some function f and some real number... Problem 83E: Derivatives from limits The following limits represent f(a) for some function f and some real number... Problem 84E: Derivatives from limits The following limits represent f (a) for some function f and some real... Problem 85E: Derivatives from limits The following limits represent f (a) for some function f and some real... Problem 86E: Derivatives from limits The following limits represent f (a) for some function f and some real... Problem 87E: Derivatives from limits The following limits represent f(a) for some function f and some real number... Problem 88E Problem 89E Problem 90E: Calculator limits Use a calculator to approximate the following limits. 66. limn(1+1n)n Problem 91E Problem 92E: Constant Rule proof For the constant function f(x) = c, use the definition of the derivative to show... Problem 93E Problem 94E: Looking ahead: Power Rule for negative integers Suppose n is a negative integer and f(x) = xn. Use... Problem 95E Problem 96E: Computing the derivative of f(x) = ex a. Use the definition of the derivative to show that... Problem 97E Problem 98E: Computing the derivative of f(x) = x2ex a. Use the definition of the derivative to show that... format_list_bulleted
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