Section You should be able to… Example Review Exercises
3.1 1 Differentiate a composite function (p. 198) 1-5 1, 13, 24
2 Differentiate \(y = a^{x},\) \(a > 0,\) \(a≠ 1\) (p. 202) 6 19, 22
3 Use the Power Rule for functions to find a derivative (p. 202) 7, 8 1, 11, 12, 14, 17
4 Use the Chain Rule for multiple composite functions (p. 204) 9 15, 18, 61
3.2 1 Find a derivative using implicit differentiation (p. 209) 1-4 43-52, 73, 81
2 Find higher-order derivatives using implicit differentiation (p. 212) 5 49-52
3 Differentiate functions with rational exponents (p. 213) 6, 7 2-8, 15, 16, 61-64
4 Find the derivative of an inverse function (p. 214) 8 53, 54
5 Differentiate inverse trigonometric functions (p. 216) 9, 10 32-38
3.3 1 Differentiate logarithmic functions (p. 222) 1-3 20, 21, 23, 25-30, 52, 72
2 Use logarithmic differentiation (p. 225) 4-7 9, 10, 31, 71
3 Express \(e\) as a limit (p. 227) 8 55, 56
3.4 1 Find the differential of a function and interpret it geometrically (p. 230) 1 65, 69, 70
2 Find the linear approximation to a function (p. 232) 2 67
3 Use differentials in applications (p. 233) 3, 4 66, 68
4 Use Newton’s Method to approximate a real zero of a function (p. 234) 5, 6 78-80
3.5 1 Find a Taylor Polynomial (p. 240) 1-3 74-77
3.6 1 Define the hyperbolic functions (p. 243) 1 57, 58
2 Establish identities for hyperbolic functions (p. 244) 2 59, 60
3 Differentiate hyperbolic functions (p. 245) 3, 4 39-41
4 Differentiate inverse hyperbolic functions (p. 246) 5-7 42