Math 12
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2.1 Introduction
2.1 Introduction
2.1.1 Average rate of Change
2.1.2 Derivative of a Function
2.2 Finding f(x) from definition of Derivative
2.2 Finding f(x) from definition of Derivative
2.2.1 Derivation of xn where neZ
2.2.2 Differentiation of Expressions of the types
Exercise 2.1
Exercise 2.2
2.3 Theorems on Differentiation
Derivative of a sum or a Difference of Functions
Derivative of a product (The product Rule)
Derivative of a Quotient (The Quotient Rule)
Exercise 2.3
2.4 The Chain Rule
2.5 Derivatives of Inverse Funtions
2.6 Derivative of a Function given in the form of Parametric Equations
2.7 Differentiation of Implicit Relations
Exercise 2.4
2.8 Derivatives of Trigonometric Functions
2.9 Derivatives of inverse Trigonometric Functions
Exercise 2.5
2.10 Derivative of Exponential Functions
2.11 Derivative of the Logarithmic Function
2.12 Logarithmic Differentiation
2.13 Derivative of Hyperbolic Functions
2.14 Derivatives of the inverse Hyperbolic Functions
Exercise 2.6
2.15 Successive Differentiation (or Higher Derivatives)
Exercise 2.7
2.16 Series Expansions of Functions
2.17 Tailor Series Expansions of Funtions
Exercise 2.8
2.18 Geometrical Interpretation of a Derivative
2.19 Increasing and Decreasing Functions
2.20 Relative Extrema
2.21 Critical Values and Critical Points
Second Derivative Test
Exercise 2.9
Application of Maxima and Minima
Exercise 2.10
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