1 Functions 2 Limits And Continuity 3 Derivatives 4 Application Of Derivatives 5 Integrals 6 Applications Of Definite Integrals 7 Integrals And 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 Derivatives Of Inverse Functions And Logarithms 3.9 Inverse Trigonometric Functions 3.10 Related Rates 3.11 Linearization And Differentials Chapter Questions expand_more
Problem 1E: Derivative Calculations
In Exercises 112, find the first and second derivatives.
1. y = − x2 + 3
Problem 2E: Derivative Calculations
In Exercises 112, find the first and second derivatives.
2. y = x2 + x+ 8
Problem 3E: Derivative Calculations
In Exercises 112, find the first and second derivatives.
3. s = 5t3 – 3t5
Problem 4E: Derivative Calculations
In Exercises 112, find the first and second derivatives.
4. w = 3ɀ7 – 7ɀ3 +... Problem 5E: Derivative Calculations
In Exercises 112, find the first and second derivatives.
Problem 6E: Derivative Calculations
In Exercises 112, find the first and second derivatives.
Problem 7E: Derivative Calculations
In Exercises 112, find the first and second derivatives.
Problem 8E: Derivative Calculations
In Exercises 112, find the first and second derivatives.
Problem 9E: Derivative Calculations
In Exercises 112, find the first and second derivatives.
9. y = 6x2 10x ... Problem 10E: Derivative Calculations
In Exercises 112, find the first and second derivatives.
10. y = 4 − 2x −... Problem 11E: Derivative Calculations
In Exercises 112, find the first and second derivatives.
11.
Problem 12E: Derivative Calculations
In Exercises 112, find the first and second derivatives.
Problem 13E: In Exercises 1316, find y'(a) by applying the Product Rule and (b) by multiplying the factors to... Problem 14E: In Exercises 1316, find y' (a) by applying the Product Rule and (b) by multiplying the factors to... Problem 15E: In Exercises 1316, find y' (a) by applying the Product Rule and (b) by multiplying the factors to... Problem 16E Problem 17E: Find the derivatives of the functions in Exercises 17 40.
Problem 18E: Find the derivatives of the functions in Exercises 17 40.
18.
Problem 19E Problem 20E Problem 21E Problem 22E Problem 23E: Find the derivatives of the functions in Exercises 1740.
23. f(s) =
Problem 24E: Find the derivatives of the functions in Exercises 1740.
24. u =
Problem 25E: Find the derivatives of the functions in Exercises 1740.
25. v =
Problem 26E Problem 27E Problem 28E Problem 29E: Find the derivatives of the functions in Exercises 17-40.
29. y = 2e−x + e3x
Problem 30E: Find the derivatives of the functions in Exercises 1740.
30. y =
Problem 31E: Find the derivatives of the functions in Exercises 17-40.
31. y = x3ex
Problem 32E: Find the derivatives of the functions in Exercises 17-40.
32. w = re−r
Problem 33E Problem 34E: Find the derivatives of the functions in Exercises 17-40.
34. y = x−3/5 + π3/2
Problem 35E: Find the derivatives of the functions in Exercises 17-40.
35. s = 2t3/2 + 3e2
Problem 36E: Find the derivatives of the functions in Exercises 17-40.
36.
Problem 37E Problem 38E Problem 39E: Find the derivatives of the functions in Exercises 1740.
39. r =
Problem 40E Problem 41E: Find the derivatives of all orders of the functions in Exercises 4144.
41. y =
Problem 42E: Find the derivatives of all orders of the functions in Exercises 41 44.
42. y =
Problem 43E Problem 44E Problem 45E Problem 46E: Find the first and second derivatives of the functions in Exercises 4552.
46. s =
Problem 47E Problem 48E Problem 49E Problem 50E Problem 51E Problem 52E Problem 53E Problem 54E Problem 55E: Normal line to a curve Find an equation for the line perpendicular to the tangent line to the curve... Problem 56E Problem 57E: Find the tangent lines to Newton’s serpentine (graphed here) at the origin and the point (1, 2).
Problem 58E: Find the tangent line to the Witch of Agnesi (graphed here) at the point (2, 1).
Problem 59E: Quadratic tangent to identity function The curve y = ax2 + bx + c passes through the point (1, 2)... Problem 60E Problem 61E: Find all points (x, y) on the graph of f(x) = 3x2 − 4x with tangent lines parallel to the line y =... Problem 62E: Find all points (x, y) on the graph of with tangent lines parallel to the line 8x − 2y = 1.
Problem 63E: Find all points (x, y) on the graph of y = x/(x − 2) with tangent lines perpendicular to the line y... Problem 64E: Find all points (x, y) on the graph of f(x) = x2 with tangent lines passing through the point (3,... Problem 65E: Assume that functions f and g are differentiable with f(1) = 2, f′(1) = −3, g(1) = 4, and g′(1) =... Problem 66E: Assume that functions f and g are differentiable with f(2) = 3, f′(2) = −1, g(2) = −4, and g′(2) =... Problem 67E: Find an equation for the line that is tangent to the curve y = x3 – x at the point (–1, 0).
Graph... Problem 68E: Find an equation for the line that is tangent to the curve y = x3 – 6x2 + 5x at the origin.
Graph... Problem 69E: For Exercises 69 and 70, evaluate each limit by first converting each to a derivative at a... Problem 70E: For Exercises 69 and 70, evaluate each limit by first converting each to a derivative at a... Problem 71E Problem 72E Problem 73E Problem 74E Problem 75E Problem 76E Problem 77E: Generalizing the Product Rule The Derivative Product Rule gives the formula
for the derivative of... Problem 78E: Power Rule for negative integers Use the Derivative Quotient Rule to prove the Power Rule for... Problem 79E: Cylinder pressure If gas in a cylinder is maintained at a constant temperature T, the pressure P is... Problem 80E format_list_bulleted