1. Chapter 3: Differentiation Topics
The Derivative
Tangent line to a curve, p.105, figures 3.1–3
Definition – differentiable (3.1.1), p. 106
Equation of the tangent line, (3.1.2), p. 109
The derivative as a function, (3.1.3), p. xxx
Tangent lines and normal lines, p. xxx, figure xxx
If f is differentiable at x, then f is continuous at x, p.111
Differentiation Formulas
Derivatives of sums, differences and scalar multiples, (3.2.3), (3.2.4), p. 115
The product rule, p. 117
The reciprocal rule, p. 119
Derivatives of powers and polynomials, (3.2.7), (3.2.8), pp. 117, 118
The quotient rule, p. 121
Derivatives of higher Order
The d/dx notation, p. 124, 125
Derivatives of higher order, p. 127
The Derivative as a Rate of Change
The Chain Rule
Leibnitz form of the chain rule, p. 133
The chain-rule theorem (3.5.6), p. 138
 Differentiating the Trigonometric Functions
Basic formulas, (3.6.1), (3.6.2), (3.6.3), (3.6.4), pp. 142, 143
The chain rule and the trig functions, (3.6.5), p. 144
My table of differentiation formulas
 Implicit differentiation; Rational Powers
Example 1, p.147, Figures 1.71–2
The derivative of rational powers, (3.7.1), p. 149
Chain-rule version, (3.7.2), p. 150
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2. The Derivative Tangent line to a curve, p. 105 - 107, figures 3.1–3
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3. The Derivative Definition – differentiable (3.1.1), p. 106
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4. The Derivative Equation of the tangent line, (3.1.2), p. 109
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5. The Derivative
If f is differentiable at x, then f is continuous at x, p. 111
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6. Differentiation Formulas
Derivatives of sums, differences and scalar multiples, (3.2.3), (3.2.4), p. 115, 116
Salas, Hille, Etgen Calculus: One and Several Variables
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7. Differentiation Formulas
The product rule, p. 117
Salas, Hille, Etgen Calculus: One and Several Variables
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8. Differentiation Formulas
The reciprocal rule, p. 119
Salas, Hille, Etgen Calculus: One and Several Variables
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9. Differentiation Formulas
Derivatives of powers and polynomials, (3.2.7), (3.2.8), pp. 117, 118
Salas, Hille, Etgen Calculus: One and Several Variables
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10. Differentiation Formulas
The quotient rule, p. 121
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11. Derivatives of Higher Order
The d/dx notation, p. 124–125
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12. Derivatives of Higher Order
Derivatives of higher order, p. 127
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13. The Derivative as a Rate of Change
The derivative as a rate of change, p. 130
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14. The Chain Rule Leibnitz form of the chain rule, p. 133
Salas, Hille, Etgen Calculus: One and Several Variables
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15. The Chain Rule The chain-rule theorem (3.5.6), p. 138
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16. Differentiating the Trigonometric Functions
Basic formulas, (3.6.1), (3.6.2), (3.6.3), (3.6.4), pp. 142, 143
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17. Differentiating the Trigonometric Functions
The chain rule and the trig functions, (3.6.5), p. 144
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18. Implicit Differentiation; Rational Powers
Example 1, p. 147, Figures 3.71–2
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19. Implicit Differentiation; Rational Powers
The derivative of rational powers, (3.7.1), p. 149
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20. Implicit Differentiation; Rational Powers
Chain-rule version, (3.7.2), p. 150
Salas, Hille, Etgen Calculus: One and Several Variables
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