Active Calculus - Gvsu - Grand Valley State University

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56 2.6. DERIVATIVES OF INVERSE FUNCTIONSActivity 2.18.Determine the derivative of each of the following functions.(a) f(x) = x 3 arctan(x) + e x ln(x)(b) p(t) = 2 t arcsin(t)(c) h(z) = (arcsin(5z) + arctan(4 − z)) 27(d) s(y) = cot(arctan(y))(e) m(v) = ln(sin 2 (v) + 1)( ) ln(w)(f) g(w) = arctan1 + w 2⊳
2.7. DERIVATIVES OF FUNCTIONS GIVEN IMPLICITLY 572.7 Derivatives of Functions Given ImplicitlyPreview Activity 2.7. Let f be a differentiable function of x (whose formula is not known) and recallthat ddx [f(x)] and f ′ (x) are interchangeable notations. Determine each of the following derivativesof combinations of explicit functions of x, the unknown function f, and an arbitrary constantc.(a)(b)(c)(d)(e)d [x 2 + f(x) ]dxd [x 2 f(x) ]dxd [c + x + f(x)2 ]dxd [f(x 2 ) ]dxd[xf(x) + f(cx) + cf(x)]dx⊲⊳
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Active CalculusMatt Boelkins, Lead
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Chapter 1Understanding the Derivati
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1.1. HOW DO WE MEASURE VELOCITY? 3A
Page 9 and 10: 1.2. THE NOTION OF LIMIT 51.2 The n
Page 11 and 12: 1.2. THE NOTION OF LIMIT 7Activity
Page 13 and 14: 1.3. THE DERIVATIVE OF A FUNCTION A
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Page 17 and 18: 1.4. THE DERIVATIVE FUNCTION 131.4
Page 19 and 20: 1.4. THE DERIVATIVE FUNCTION 15rsxx
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Page 25 and 26: 1.6. THE SECOND DERIVATIVE 21(a) In
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Page 31 and 32: 1.7. LIMITS, CONTINUITY, AND DIFFER
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Page 35 and 36: 1.8. THE TANGENT LINE APPROXIMATION
Page 37 and 38: Chapter 2Computing Derivatives2.1 E
Page 39 and 40: 2.1. ELEMENTARY DERIVATIVE RULES 35
Page 41 and 42: 2.2. THE SINE AND COSINE FUNCTIONS
Page 43 and 44: 2.2. THE SINE AND COSINE FUNCTIONS
Page 45 and 46: 2.3. THE PRODUCT AND QUOTIENT RULES
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Page 49 and 50: 2.4. DERIVATIVES OF OTHER TRIGONOME
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Page 53 and 54: 2.5. THE CHAIN RULE 492.5 The chain
Page 55 and 56: 2.5. THE CHAIN RULE 51Activity 2.14
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Page 69 and 70: Chapter 3Using Derivatives3.1 Using
Page 71 and 72: 3.1. USING DERIVATIVES TO IDENTIFY
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Page 75 and 76: 3.2. USING DERIVATIVES TO DESCRIBE
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Page 79 and 80: 3.3. GLOBAL OPTIMIZATION 75Activity
Page 81 and 82: 3.3. GLOBAL OPTIMIZATION 77Activity
Page 83 and 84: 3.4. APPLIED OPTIMIZATION 79Activit
Page 85 and 86: 3.4. APPLIED OPTIMIZATION 81Activit
Page 87 and 88: 3.5. RELATED RATES 833.5 Related Ra
Page 89 and 90: 3.5. RELATED RATES 85Activity 3.15.
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Page 93 and 94: Chapter 4The Definite Integral4.1 D
Page 95 and 96: 4.1. DETERMINING DISTANCE TRAVELED
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Page 99 and 100: 4.2. RIEMANN SUMS 95⊲⊳
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Page 109 and 110: 4.4. THE FUNDAMENTAL THEOREM OF CAL
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4.4. THE FUNDAMENTAL THEOREM OF CAL
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Active Calculus - Gvsu - Grand Valley State University

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