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   Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

The Derivative Tangent line to a curve, p. 105 - 107, figures 3.1–3 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

The Derivative Definition – differentiable (3.1.1), p. 106 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

The Derivative Equation of the tangent line, (3.1.2), p. 109 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

The Derivative If f is differentiable at x, then f is continuous at x, p. 111 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

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 Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

Differentiation Formulas The product rule, p. 117 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

Differentiation Formulas The reciprocal rule, p. 119 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

Differentiation Formulas Derivatives of powers and polynomials, (3.2.7), (3.2.8), pp. 117, 118 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

Differentiation Formulas The quotient rule, p. 121 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

Derivatives of Higher Order The d/dx notation, p. 124–125 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

Derivatives of Higher Order Derivatives of higher order, p. 127 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

The Derivative as a Rate of Change The derivative as a rate of change, p. 130 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

The Chain Rule Leibnitz form of the chain rule, p. 133 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

The Chain Rule The chain-rule theorem (3.5.6), p. 138 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

Differentiating the Trigonometric Functions Basic formulas, (3.6.1), (3.6.2), (3.6.3), (3.6.4), pp. 142, 143 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

Differentiating the Trigonometric Functions The chain rule and the trig functions, (3.6.5), p. 144 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

Implicit Differentiation; Rational Powers Example 1, p. 147, Figures 3.71–2 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

Implicit Differentiation; Rational Powers The derivative of rational powers, (3.7.1), p. 149 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.

Implicit Differentiation; Rational Powers Chain-rule version, (3.7.2), p. 150 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved.