Problem 1E: In Exercises 1–4:
Find f–1(x).
Graph f and f–1 together.
Evaluate df/dx at x = a and df–1/dx at x =... Problem 2E: In Exercises 1–4:
Find f–1(x).
Graph f and f–1 together.
Evaluate df/dx at x = a and df–1/dx at x =... Problem 3E: In Exercises 1–4:
Find f–1(x).
Graph f and f–1 together.
Evaluate df/dx at x = a and df–1/dx at x =... Problem 4E Problem 5E: Show that f(x) = x3 and are inverses of one another.
Graph f and g over an x-interval large enough... Problem 6E Problem 7E: Let f(x) = x3 – 3x2 – 1, x ≥ 2. Find the value of df–1/dx at the point x = –1 = f(3).
Problem 8E Problem 9E: Suppose that the differentiable function y = f(x) has an inverse and that the graph of f passes... Problem 10E Problem 11E: Derivatives of Logarithms
In Exercises 11–40, find the derivative of y with respect to x, t, or θ,... Problem 12E: Derivatives of Logarithms
In Exercises 11–40, find the derivative of y with respect to x, t, or θ,... Problem 13E: Derivatives of Logarithms
In Exercises 11–40, find the derivative of y with respect to x, t, or θ,... Problem 14E: Derivatives of Logarithms
In Exercises 11–40, find the derivative of y with respect to x, t, or θ,... Problem 15E: Derivatives of Logarithms
In Exercises 11–40, find the derivative of y with respect to x, t, or θ,... Problem 16E: Derivatives of Logarithms
In Exercises 11–40, find the derivative of y with respect to x, t, or θ,... Problem 17E Problem 18E: Derivatives of Logarithms
In Exercises 11-40, find the derivative of y with respect to x, t, or θ,... Problem 19E: Derivatives of Logarithms
In Exercises 11-40, find the derivative of y with respect to x, t, or θ,... Problem 20E Problem 21E: Derivatives of Logarithms
In Exercises 11-40, find the derivative of y with respect to x, t, or θ,... Problem 22E: Derivatives of Logarithms
In Exercises 11-40, find the derivative of y with respect to x, t, or θ,... Problem 23E Problem 24E: In Exercises 11-40, find the derivative of y with respect to x, t, or θ, as appropriate.
24. y = (x2... Problem 25E: In Exercises 11-40, find the derivative of y with respect to x, t, or θ, as appropriate.
25.
Problem 26E Problem 27E: In Exercises 11-40, find the derivative of y with respect to x, t, or θ, as appropriate.
27.
Problem 28E: In Exercises 11-40, find the derivative of y with respect to x, t, or θ, as appropriate.
28.
Problem 29E: In Exercises 11-40, find the derivative of y with respect to x, t, or θ, as appropriate.
29. y = ln... Problem 30E Problem 31E Problem 32E Problem 33E: In Exercises 11-40, find the derivative of y with respect to x, t, or θ, as appropriate.
33.
Problem 34E: In Exercises 11-40, find the derivative of y with respect to x, t, or θ, as appropriate.
34.
Problem 35E: In Exercises 11-40, find the derivative of y with respect to x, t, or θ, as appropriate.
35.
Problem 36E: In Exercises 11-40, find the derivative of y with respect to x, t, or θ, as appropriate.
36.
Problem 37E Problem 38E: In Exercises 11-40, find the derivative of y with respect to x, t, or θ, as appropriate.
38.
Problem 39E Problem 40E Problem 41E: In Exercises 41-54, use logarithmic differentiation to find the derivative of y with respect to the... Problem 42E Problem 43E: In Exercises 41-54, use logarithmic differentiation to find the derivative of y with respect to the... Problem 44E Problem 45E Problem 46E Problem 47E: In Exercises 41-54, use logarithmic differentiation to find the derivative of y with respect to the... Problem 48E: In Exercises 41-54, use logarithmic differentiation to find the derivative of y with respect to the... Problem 49E Problem 50E Problem 51E: In Exercises 41-54, use logarithmic differentiation to find the derivative of y with respect to the... Problem 52E Problem 53E: In Exercises 41-54, use logarithmic differentiation to find the derivative of y with respect to the... Problem 54E Problem 55E Problem 56E Problem 57E: In Exercises 55-62, find the derivative of y with respect to x, t, or θ, as appropriate.
57. y = ln... Problem 58E Problem 59E: In Exercises 55-62, find the derivative of y with respect to x, t, or θ, as appropriate.
59.
Problem 60E Problem 61E Problem 62E Problem 63E Problem 64E Problem 65E Problem 66E Problem 67E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
67. y =... Problem 68E Problem 69E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
69.
Problem 70E: In Exercises 67–88, find the derivative of y with respect to the given independent variable.
70.
Problem 71E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
71. y =... Problem 72E Problem 73E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
73. y =... Problem 74E Problem 75E Problem 76E Problem 77E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
77. y =... Problem 78E Problem 79E Problem 80E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
80.
Problem 81E Problem 82E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
82.
Problem 83E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
83. y =... Problem 84E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
84.
Problem 85E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
85.
Problem 86E Problem 87E Problem 88E Problem 89E: In Exercises 89-100, use logarithmic differentiation or the method in Example 7 to find the... Problem 90E Problem 91E Problem 92E Problem 93E Problem 94E: In Exercises 89−100, use logarithmic differentiation or the method in Example 7 to find the... Problem 95E: In Exercises 89−100, use logarithmic differentiation or the method in Example 7 to find the... Problem 96E Problem 97E Problem 98E: In Exercises 89−100, use logarithmic differentiation or the method in Example 7 to find the... Problem 99E: In Exercises 89−100, use logarithmic differentiation or the method in Example 7 to find the... Problem 100E: In Exercises 89−100, use logarithmic differentiation or the method in Example 7 to find the... Problem 101E Problem 102E: Show that for any x > 0.
Problem 103E: If f(x) = xn, n ≥ 1, show from the definition of the derivative that f′(0) = 0.
Problem 104E: Using mathematical induction, show that for n > 1,
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